An uncompromising Binyamin Netanyahu struggled to repair relations with US liberals on Tuesday in a visit to the heart of the Democratic establishment that was billed as a bridge-building exercise but was noticeable for the Israeli prime minister’s entrenched positions.

During an hour of questions at the Center for American Progress in Washington, Netanyahu sounded a gloomy note about prospects for peace with the Palestinians, although he insisted he still favoured a two-state solution in theory.

“The question of Jerusalem, specifically the Temple Mount, I think is insoluble,” he said. “It has to remain under Israeli sovereignty and that’s the only way to prevent it from exploding,” Netanyahu told one questioner, Morton Halperin, the chair of the board of directors at liberal lobby group J Street.

In another exchange, the prime minister insisted Israeli troops would also have to remain on the West Bank to provide security under any future peace deal, but admitted this was unlikely to be considered acceptable.

“Any deal ... must have Israel maintain the ability to defend itself; that’s the most important provision,” Netanyahu told David Makovsky of the Washington Institute, one of three lobbyists who were the only guests able to ask questions.

“That’s not something I see the Palestinians accepting now. Maybe they will accept it tomorrow,” he added, comparing such a long-term security presence to allied bases in Germany and Japan after the second world war.

The Israeli government had billed Netanyahu’s visit to Washington – his first since a controversial speech to Congress in March calling on it to block Obama’s talks with Iran – as a chance to mend relations with Democrats who fear he has strained the bipartisan consensus over support for Israel by siding with Republican hawks.

“I know my visit here has been the source of some controversy, so I doubly appreciate the invitation,” Netanyahu told moderator and CAP president Neera Tanden. “I think it’s vital that Israel remain an issue of bipartisan consensus. It’s crucial,” he added.

But many liberal observers were angry at CAP for allowing Netanyahu to “burnish his bipartisan credentials” without exposing him to tougher questioning.

“There are a large number of Democrats who have been really alienated by Netanyahu’s behaviour, not just over Iran but on peace talks and settlement issues and those scepticisms clearly remain after today,” said Matt Duss, president of the Foundation for Middle East Peace and a former CAP policy analyst.

In particularly, critics claim Netanyahu was able to make a number of controversial claims that were not challenged by Tanden during the session.

“I think factually there have been no new settlements built in the last 20 years; the additions are in existing communities,” said the prime minister. “The addition is one tenth of 1%, maybe three-tenths of 1%: that’s the land that is being ‘gobbled up’. It’s become an axiom that we are gobbling up land. We’re not.”

At the end of the session, Netanyahu turned to Tanden and said: “I’d like to make another suggestion: invite me again.” He was met with silence.

• This article was amended on 21 November 2015. An earlier version said incorrectly that Morton Halperin was the president of J Street.