The announcement of the new government has been delayed by demands and counter-demands over cabinet portfolios from Siniora's anti-Syrian friends and powerful allies of Damascus.
"I believe we are making progress towards forming this government," Siniora said after a meeting on Wednesday with President Emile Lahoud, a close Syria ally.
"We call on various parties to cooperate ... to remove all differences" over the makeup of the cabinet, he said.
A key stumbling block facing the formation of the government are demands by a Shia Muslim alliance loyal to Syria to appoint a Shia foreign minister.
The Hizb Allah group, which swept the Shia Muslim vote in last month's elections to win 14 parliament seats, has chosen to join the cabinet for the first time and asked Siniora for two ministerial posts.
While Siniora, a Sunni, had agreed to this, he had rejected demands by Hizb Allah and its ally, Amal, over the Foreign Ministry.
He talked with Hizb Allah chief Shaikh Hassan Nasr Allah on Tuesday night.
Political sources say Siniora wants to give the portfolio to former foreign minister Fouad Boutrous, a Christian.
The Foreign Ministry, currently run by a Shia, is seen as crucial since it is expected to play an important role in shaping ties with Damascus after Syrian troops ended their 29-year military presence in Lebanon in April.
It also oversees ties with the United Nations over implementing a Security Council resolution demanding the disarming of Hizb Allah fighters.
Aoun's bloc is likely to form
the backbone of the opposition
Siniora's talks with Lahoud, a political foe, were the first over the government since the president bowed to an overwhelming parliamentary majority last week and appointed Siniora.
While Lahoud was obliged to respect the will of the parliament, he has the power to reject Siniora's cabinet lineup or demand more of his own allies get a role.
Christian leader Michel Aoun, a long-time critic of Damascus, has said he will not be represented in the government after his demands for the Justice Ministry were turned down.
Aoun leads a 21-member bloc in parliament, where groups opposed to Syria's influence are in a majority. His bloc appears set to form the backbone of opposition to a Siniora government.
Lebanon was plunged into its worst crisis since the 1975-1990 civil war with the 14 February assassination of former prime minister Rafiq al-Hariri. His killing has been followed by a series of assassinations and bomb attacks in and around Beirut.