TEL AVIV—U.S. Secretary of State John Kerry appears to have won over an unlikely Israeli ally in his quest for an Israeli-Palestinian peace deal: Foreign Minister Avigdor Lieberman.

Known for his view that a permanent peace agreement is unrealistic, in recent days Mr. Lieberman seems to have made an about-face by giving repeated public endorsements of Mr. Kerry's diplomacy.

During a visit to the U.K. on Tuesday, Mr. Lieberman released a joint statement with British Foreign Secretary William Hague, hailing Mr. Kerry and praising the Israeli-Palestinian negotiations he has pushed as a "unique opportunity to end the conflict once and for all."

On Sunday, in remarks to a seminar of Israeli ambassadors in London, he suggested that Mr. Kerry's proposals for a broad peace compromise—known as a framework— figure as the friendliest Israel can hope for from the international community. "We cannot ignore the effort and the substance of the positions that Kerry brought with him on security arrangements, also the issue of a Jewish state and on other issues," he said. "It must be understood that any other offer from the international community will be much less comfortable for us. Kerry is worthy of all the appreciation from us."

As one of Israeli Prime Minister Benjamin Netanyahu's top allies, the foreign minister's backing would boost the prime minister's efforts to hold together a coalition that is showing signs of fracturing over the politically painful compromises Mr. Kerry has been hinting at.

However, Mr. Lieberman said any deal with the Palestinians should include "population swap," a controversial proposal to allow Israel to annex Jewish settlers and cede towns with hundreds of thousands of Israeli Arab citizens to the Palestinian state. That proposal, aimed at shrinking Israel's Arab minority, has no other prominent backers.

Mr. Lieberman recently returned to the foreign ministry after being acquitted of corruption charges that sidelined him for a year.

Though Mr. Lieberman chalked up a lengthy dossier of undiplomatic remarks toward the international community during his first term in office, Israeli political experts note he is a pragmatist who, despite a hard-liner reputation and a home address in the Jewish settlements, has never been ideologically opposed to ceding land to the Palestinians as are many of the parliament members in Mr. Netanyahu's own party.

After testy relations with the U.S. administration during his first term in office, His embrace of Mr. Kerry is seen by some Israeli political experts as an effort to make himself more relevant on the international stage and even outflank Mr. Netanyahu, who clashed with the Obama administration.

"Kerry realizes [Mr. Lieberman's] cooperation is crucial. Every time he says something good about Kerry, you have to realize that two years ago he would have been saying something bad about [Abbas],'' said Tal Shalev, the diplomatic correspondent for i24 News, an Israeli news channel.

"At some point he'll want to compete for leadership, and he realizes at least compared to Netanyahu's bad relationship with the U.S., it could be an asset for him in the future…. Nobody gains anything in Israeli politics with opposing the U.S. out loud.''

Israeli political commentators said Tuesday that Mr. Kerry met separately with Mr. Lieberman during his latest round of shuttle diplomacy over the weekend, signaling an effort by the secretary of state to build a political coalition around Mr. Netanyahu to support a peace deal.

While Mr. Netanyahu has personally questioned the commitment of Palestinian President Mahmoud Abbas to the peace process in recent days, and made allegations about official Palestinian incitement against Israel, Mr. Lieberman has remained mum.

An Israeli official said he believes the change in tone goes beyond optics. "He is saying things that are committing himself'' to negotiations, said the official. "I don't think he's changed his mind about [Palestinian President Mahmoud Abbas], but he understands there's no wisdom in saying out loud what he really believes.''