However, Israel rejected the criticism, with Mark Regev, the Israeli government spokesman, saying on Thursday that "normal life" would be allowed to continue in West Bank settlements, effectively meaning construction would continue to accommodate population growth.
Clinton said it was in the "best interest" of peace efforts that settlement expansion cease.
"That is our position. That is what we have communicated very clearly not only to the Israelis but to the Palestinians and others. And we intend to press that point," she said on Wednesday after meeting Abbas.
But Regev said that settlement activity would continue as usual and that the fate of settlements "will be determined in final status negotiations between Israel and the Palestinians and in the interim, normal life must be allowed to continue in those communities".
Speaking to Al Jazeera, he said that the Arab world and Palestinians had their own obligations for peace to be cemented in the region and it was not fair to put all the blame on Israel.
"I'm not in any way shirking Israel's obligations, what I'm saying is we have to see Palestinians and Arab states move forward on their obligations as well - that's a key to a healthy peace process," he said.
Al Jazeera's Nour Odeh, speaking from Ramallah in the West Bank, said Abbas plans to present Obama with a detailed plan not just of a Palestinian vision for peace but also for peace in the wider region, based on the Arab peace initative and other proposals.
He will also be asking for specific steps to be taken, including urging Israel to commit to a two-state solution and to end all settlement activity, she said.
Saeb Erekat, the chief Palestinian negotiator, told Al Jazeera that while the Palestinians appreciated Clinton's statement, they hoped the US would get Israel to "comply".
"Settlements are illegal and illegal things don't have natural growth and should not have natural growth and it's really shameful to continue throwing [out] this line and at the same to time to speak about a two state solution," he said.
|Israeli settlements are considered ilegal
under international law [EPA]
"Israel has the choice - settlements or peace. They can't have both."
The talks between Obama and Abbas are the latest in a series of diplomatic moves by the Obama administration over the Israeli-Palestinian conflict.
They follow talks in Washington between Obama and Netanyahu last week, and a meeting between Obama and King Abdullah of Jordan in April.
Al Jazeera's Rob Reynolds, reporting from Washington, said Thursday's meeting will prove crucial for Obama as finding a resolution to the conflict is key to Washington's wider aims in the region, such as removing the impetus for radicalism and restricting the growth of Iran's power.
In addition, the meeting is a chance for Obama to legitimise Abbas as opposed to members of the Palestinian group Hamas, although he has to take a fine line of not making the Palestinian president appear to be a puppet of Washington, our correspondent said.
Abbas has ruled out restarting long-stalled peace talks until Israel halts all settlement activity.
But less than a week after meeting Obama, aides quoted Netanyahu as telling his cabinet that while he did not intend to build new settlements, "it makes no sense to ask us not to answer to the needs of natural growth and to stop all construction".
"Natural growth" is a term used by Israelis to describe construction inside existing settlements that they say is necessary for the needs of growing settler families.
Netanyahu has also resisted committing to a two-state solution to the Israeli-Palestinian conflict, focusing his talks with Obama instead on Iran.
The Palestinians say settlements built on land Israel occupied in the 1967 Middle East war, and deemed illegal internationally, could deny them a viable and contiguous state and that expansion activities undermine efforts to negotiate a peace agreement.
Outposts are smaller settlements, often just a group of trailers inhabited by a few dozen people, built without Israeli government authorisation but often given infrastructural support by the government.
Israeli media reported earlier in the week that Netanyahu was willing to tear down outposts in the occupied West Bank in return for US backing on its stance on Iran.
About 500,000 Israeli setters live in more than 100 settlements that Israel has built since its 1967 occupation of the West Bank and East Jerusalem, territory in which close to three million Palestinians live.
Under the US-backed 2003 "road map" peace plan, Israel is supposed to end all settlement activity, including natural growth, while the Palestinian Authority is supposed to crack down on armed groups who seek to attack Israelis.
The two sides accuse each other of not fulfiling its obligations under the plan.