When Yitzhak Shamir became the prime minister of Israel in 1983, after the resignation of Menachem Begin, many saw the hardline leader of the Likud party as a compromise choice and predicted that he would soon be shunted aside. They were to be proved wrong.

Shamir, who has died aged 96, became Israel's second longest serving prime minister (after David Ben-Gurion), and perhaps its most rightwing leader. Shamir lacked the charisma and political experience of his predecessor. But he grew into the job, maintaining Begin's tough stance on the Palestinian issue and displaying patience, or at least the uncanny ability to postpone unpleasant decisions.

Days after Shamir became prime minister, the Tel Aviv stock market collapsed. His emergency measures only partly succeeded. The faltering economy, and disenchantment over the invasion of Lebanon, deprived him of a total victory in the 1984 polls and forced him into a coalition with Shimon Peres's Labour party. Under a rotation agreement, Shamir served as foreign minister under Peres for two years, then resumed the premiership himself in 1986. Israel's government was speaking with two voices – sheer farce to many Israelis, and a wasted opportunity for those who sought real peace.

The clearest instance of division was when Shamir countermanded Peres's so-called London Agremeent for an international peace conference, arranged with King Hussein of Jordan and secretly signed in the London home of the lawyer Lord Mischon in 1987. In 1986, Shamir resumed the premiership.

The 1988 election was fought against the backdrop of the intifada (the Palestinian uprising against Israel in the occupied territories). Another inconclusive result ensued, and Shamir headed an increasingly shaky coalition that rejected the putative peace overtures of the Palestine Liberation Organisation (PLO). In 1989, his cabinet colleagues bullied Shamir into curtailing his modest plans for local elections in Palestine, but he regained prestige by championing the influx of Soviet Jews to Israel.

In 1990, the coalition broke apart in disagreement over US proposals for peace between Israel and Palestine, and months of unprecedented horse-trading followed. When Peres failed to form a Labour government, Shamir fashioned a rightwing coalition with support from religious parties. Unhindered by Labour's restraining hand, he promoted Jewish settlements in the occupied territories, which he pointedly called Judea and Samaria.

During the Gulf war of 1991, Shamir was restrained in the face of Iraqi scud attacks on Israel – winning approval from the US for not retaliating against Iraq, and thereby potentially destroying the anti-Saddam coalition. In the same year, he reluctantly took part in peace talks in Madrid with Israel's Arab neighbours and the Palestinians. Ironically, this most rightwing Israeli premier became the first to openly negotiate with Palestinians, and thus set in train a process which led to Israel's historic recognition of the PLO and Palestinians' right to autonomy.

Also in 1991, Shamir displayed rare flair in evacuating more than 14,000 Ethiopian Jews overnight to Israel in the airlift known as Operation Solomon.

But at the 1992 election, Labour's "land-for-peace" stance on the Palestinians struck a chord with voters and Yitzhak Rabin took office. Shamir had neglected social policy and failed to nurture Likud's Sephardi (oriental Jewish) supporters. The margin of Rabin's electoral victory (35% of votes compared with Shamir's 25%) surprised even the Labour leader. Shamir reluctantly resigned as party leader and was succeeded, in 1993, by Binyamin Netanyahu, a fellow hawk but a generation younger. Within three years, Netanyahu was prime minister.

Shamir was born Yitzhak Yezernitsky in the small town of Ruzinoy, Poland (now Ruzhany, in Belarus). He attended a Hebrew secondary school in Białystok, where his father was a teacher, and then studied law at Warsaw University. As a devoutly rightwing Revisionist Zionist, he emigrated to Palestine, then under the British mandate, in 1935. He adopted the Hebrew surname of Shamir (which means "thorn"). In 1937 he joined the Irgun Zvai Leumi militia (later led by Begin). The group despised the liberal socialism of the dominant Labour Zionists and its goal was an "Iron Wall" to defend Jews against what they deemed would be an inevitable backlash by Arabs. They also strove for a Jewish state on both banks of the Jordan.

During the second world war, Shamir's mother and sister were killed in the Holocaust. Despite this, he seldom invoked the Holocaust in his rhetoric, and felt uncomfortable when his mentor, Begin, did so.

While most Palestinian Jews upheld a wartime ceasefire with British mandate authorities, Shamir helped found an extreme Irgun breakaway faction called Lehi. He joined its leadership troika after Lehi's chief, Avraham Stern, was killed in 1942. Shamir plotted the assassinations of Lord Moyne, British minister for Middle East affairs, in Cairo in 1944, and of the UN negotiator Count Folke Bernadotte, in Jerusalem in 1948.

He was also implicated in the bombing of the King David hotel, the British headquarters in Jerusalem, in 1946. He was arrested that year, and interned in British-ruled Eritrea, but he escaped and made his way to France, where he was given political asylum. He returned to Israel in 1948, the year it achieved independence.

Shamir became a businessman and, from 1955 to 1965, served as aide to the chief of Mossad. His command of languages, ruthless diligence and ability to mingle in a crowd were clear assets. His Mossad career ended after he led an abortive rebellion against its leadership. He joined the Herut party (which later merged into Likud) in 1970 and, despite his late start in politics, won a seat in the Knesset in 1973 and rose rapidly within influential committees. Though he was never renowned as an orator he was elected chairman of the Herut executive.

After Likud won power for the first time in 1977, Begin, the prime minister, made Shamir the speaker of the Knesset. Shamir initially opposed the Camp David accords with Egypt and the subsequent peace treaty in 1979, but later changed his mind. Was this a first inkling of moderation or merely his legendary pragmatism in action? Whatever the case, Shamir became foreign minister after Moshe Dayan resigned in 1980.

Shamir was a member of the inner cabinet coterie that planned Israel's 1982 invasion of Lebanon. Evidently he had qualms but never spoke out decisively. The Kahan Commission of inquiry into the massacres of Palestinians at the Sabra and Shatila refugee camps that year gave Shamir little more than a rap over the knuckles, while the defence minister, Ariel Sharon, resigned from his position. When an exhausted Begin resigned in 1983, leaving no obvious successor, it was Shamir and not Sharon who carried the hard-liners' banner.

In 1944, Shamir married Shulamit Levy. She died in 2011. He is survived by his daughter, Gilada, his son, Yair, five grandchildren and seven great-grandchildren.

• Yitzhak Shamir, politician, born 15 October 1915; died 30 June 2012