Lahoud had adopted the measure "given the exceptional circumstances and in the interest of the country".
Siniora promptly said Lebanon's government rejected the move as "unconstitutional".
He said his government will continue to exercise its powers after Lahoud's mandate expires.
"The government is legitimate and constitutional," he said in a statement.
Lebanon's constitution stipulates that if there is no new president, his powers are automatically transferred to the government - currently of Siniora.
But Lahoud and the opposition - both backed by Syria - have considered Siniora's Western-backed government as illegitimate since the resignation of all Shia cabinet members last year.
Earlier on Friday, a vote to elect a successor to Lahoud was postponed after the Hezbollah-led opposition threatened to boycott the poll.
The parliamentary vote set for Friday was put off for a week, the office of Nabih Berri, the parliament speaker, said just hours before politicians were scheduled to cast their ballots.
The vote had been the last chance to choose a president before Lahoud left office.
Many Lebanese fear the failure to elect a president could throw the country deeper into political chaos and violence.
However, speaking to Al Jazeera, Nadim Shahada, a political analyst in Beirut, said: "In a way, the Lebanese have shown they have a very healthy political system. In most countries this could be considered normal politics. There is no appetite for civil war.
|Some young Lebanese celebrate |
the end of Lahoud's term [AFP]
In a statement read on his behalf, Berri said: "To allow for more consultations to arrive at the election of a president ... the session is postponed to Friday, November 30."
The opposition had earlier said it would not take part in the session, denying the chamber the necessary two-thirds quorum.
Four previous sessions in the last two months to pick Lahoud's successor were also called off because of the ongoing standoff.
Politicians from the ruling coalition and the opposition have been unable to agree on a compromise presidential candidate, prompting fears of a power vacuum or the formation of two rival governments, as was the case at the end of the 1975-1990 civil war.
The army was deployed heavily in the capital on Friday, with tanks and troops at all major intersections, and the downtown area where the parliament building is located was declared off-limits.
Extra security measures were taken around a five-star hotel where dozens of MPs from the parliamentary majority have been under guard for the past two months for fear of assassination.
The ruling coalition, which has 68 deputies in the 127-member parliament, had repeatedly vowed to proceed with a simple majority vote if no agreement is reached.
But Hassan Nasrallah, the Hezbollah leader, said that any attempt by the ruling coalition, which has a slim majority in parliament, would be tantamount to a coup.
The standoff between Siniora's government and Hezbollah began after the Shia group, empowered by its 34-day war with Israel last year, pulled its five ministers from the cabinet in November 2006.
The army has warned against internal strife and both sides accuse the other of arming their supporters.