According to a statement released by his office on Tuesday, Lahoud told reporters on his flight to New York the day before that he would finish his term despite calls for his resignation.
"The important thing is that everybody hears our voice. This is in the interest of Lebanon," Lahoud said of his departure for New York in the midst of a UN probe into the 14 February al-Hariri assassination.
Many Lebanese politicians have said Lahoud bears at minimum political responsibility for the slaying, and his foes urged him to stay home while the investigation continued.
"If a human being had a bloody history, he can commit such a crime. But if his hands were not tainted with blood, then his conscience is clear and my conscience is clear," Lahoud said.
Nevertheless, four of his top generals, including his Presidential Guard commander, have been arrested in the investigation.
Lahoud said he would not protect the commanders who had been arrested.
"We must know the criminals and I will erect their gallows with my hands. We should not make this topic harm the interest of Lebanon"
"We must know the criminals and I will erect their gallows with my hands. We should not make this topic harm the interest of Lebanon," the president said.
But in a sign that Lahoud is being isolated internationally, US President George Bush did not invite him to a New York reception for foreign leaders later this week.
Diplomats have said US Secretary of State Condoleezza Rice has also left Lahoud off the guest list for her reception on the sidelines of the UN summit, despite meeting him when she visited Beirut in July.
Washington opposed last September's three-year extension of Lahoud's term under Syrian pressure.
A former commander of Lebanon's armed forces, Lahoud has often criticised US policy on the Arab-Israeli conflict since coming to office in 1998.
But his position has become increasingly difficult since Syria was forced to withdraw its troops from Lebanon at the end of April, and the elections in May and June ousted the so-called pro-Syrian majority in parliament.