Donald Trump has dropped a two-decades old US commitment to the establishment of a Palestinian state alongside Israel as part of a permanent Middle East peace agreement.

Speaking at a joint press conference with the Israeli prime minister, Benjamin Netanyahu, the US president did not rule out a two-state solution but implied his administration had no ­preference when it came to the final ­geography of the region as part of a ­permanent Middle East peace agreement.

Asked what he thought about a two-state solution on Wednesday, Trump said: “I’m looking at two-state and one-state and I like the one that both parties like. I’m very happy with the one that both parties like,” he said.

Trump’s comments dismantled one of the key pillars of the US-led peace efforts since before the signing of the Oslo accords, which envisioned the creation of a Palestinian state alongside the Jewish one.

“The United States will encourage peace and really a great peace deal,” the US president said. “We will be working on it very, very diligently. But it is the parties themselves who must directly negotiate such an agreement.

“To be honest, if Bibi [Netanyahu] and the Palestinians, if Israel and the Palestinians are happy – I’m happy with the one they like the best.”

In an otherwise effusive welcome for his Israeli ally, Trump used the occasion to deliver a mild rebuke to Netanyahu on the pace of settlement construction, suggesting that it would be one of the compromises necessary to strike a deal.

“I’d like to see you pull back on settlements for a little bit,” he said.

The Israeli government has said it plans to build approximately 6,000 Jewish settlement housing units in the West Bank, signalling a surge in planned construction since Trump was sworn in as president in January.

Netanyahu shrugged off Trump’s comment, gave no such undertaking, and insisted that settlements were “not the core of the conflict”.

Trump castigated the Palestinians for teaching their children to “hate” Israel. But he continued to put off his pledge to move the US embassy in Israel from Tel Aviv to Jerusalem, a constant demand of the US and Israeli right, while insisting it was being considered very carefully.

And while there was tough talk from both men on Iran, Trump did not repeat earlier threats to “dismantle” the international nuclear deal agreed with Tehran in 2015.

At their first meeting since Trump’s election, both leaders expressed the hope that Arab states could be brought in to helping forge an enduring Israeli-Palestinian agreement that has eluded the region for 70 years, suggesting that those states were more amenable and friendly to Israel because of a shared fight against “radical Islamic terror” and Iranian influence.

Most long-term observers of the region have argued that the chance of Arab states in the Middle East giving up the goal of an sovereign Palestinian state was close to nil.

Neither Trump and Netanyahu, speaking before they had substantive talks, sketched out what the alternative to a two-state solution would look like – a shared non-denominational state of Jews and Arabs, or an enlarged Jewish state with a non-voting Palestinian population living in annexed territory.