Speaking after talks with Lebanese President Emile Lahoud in Beirut, the Palestinian leader said: "We are guests in Lebanon, temporary guests, and we are subject to Lebanese laws just like everybody else in Lebanon."
However, he said that his talks with Lebanese officials did not specifically deal with the issue of disarming Palestinian refugee camps in Lebanon.
Abbas arrived in the city on Friday from neighbouring Damascus where he met Syrian President Bashar al-Assad.
In addition to the meeting with Lahoud, Abbas held talks with Parliament Speaker Nabih Berri and outgoing Prime Minister Najib Mikati. He is scheduled to meet a Palestinian delegation from refugee camps in Lebanon.
During his visit, Abbas is expected to discuss the issue of disarming Palestinians living in the country as demanded by UN Security Council resolution 1559, which calls on Lebanese and non-Lebanese groups to give up their weapons.
The resolution, issued last September, refers to the Lebanese Shia Muslim Hizb Allah resistance group - which continues to fight Israel in a small contested area near the south Lebanon border - and thousands of armed Palestinians living in 12 Palestinian camps across Lebanon.
Hizb Allah has refused to disarm and the Lebanese government, which considers the group to be a legitimate resistance group, supports its stance, saying disarmament hinges on an overall peace settlement with Israel.
Lebanon hosts more than 350,000 Palestinian refugees, including thousands of armed men from the mainstream Palestinian Fatah faction, in densely populated camps around the country that are off limits to the Lebanese government.
The authorities fear there would be bloodshed if they go into the camps, where many wanted men are known to be hiding.
There are in the region of 350,000
Palestinian refugees in Lebanon
The first refugees came to Lebanon after the 1948 war that saw the creation of Israel.
Their presence is a touchy subject and officials fear conspiracies to settle them in Lebanon, something that would upset the delicate balance among the country's 17 sects.
Palestinian officials have stressed Lebanese sovereignty and said Palestinians will not commit acts that threaten Lebanon's security.
Right of return
But Abbas would probably be heavily criticised back home for disarming them, and it could be perceived as an introduction to permanently setting the Palestinians in Lebanon.
Abbas' predecessor, the late Palestinian leader Yasser Arafat, was never willing or politically able to give up the right of return for Palestinian refugees in Arab countries.
Resolution 1559 also called for the withdrawal of the Syrian army from Lebanon, which was completed in April. However Abbas said he did not raise the matter with Lahoud.
"Resolution 1559 concerns the Lebanese government and people, and we are with them in any decision they take concerning implementation of this resolution," he said after their meeting.
Hassan Nasr Allah's Hizb Allah
has rejected US calls to disarm
Visiting US Deputy Assistant Secretary of State for Near Eastern Affairs, Elizabeth Dibble, reiterated the need for Palestinian groups to disarm, but said the Palestinian presence in Lebanon is a final status question.
"I know that this issue is a very sensitive one here in Lebanon. The issue of final status has yet to be determined by Israel and the Palestinians, and this is all tied up with that," she told Voice of Lebanon radio station.
Abbas also thanked the Lebanese government for the recent easing of labour restrictions for Palestinians born in Lebanon.
A decree issued last month by Lebanon's labour minister relaxed rules denying Palestinian refugees living in the country since the creation of Israel the right to work in most jobs, allowing them to work in a range of private-sector jobs.
"We are very grateful for the Lebanese government for this great brotherly measure," Abbas said.
Abbas said it was up to the Lebanese government to decide on an appropriate time for opening a Palestinian embassy in Beirut.