Aljazeera learned from sources close to French Foreign Minister Michel Barnier - on a visit to Washington - that Paris did not respond to the US demand and avoided talking about Hizb Allah.
After Barnier's meeting with US Secretary of State Condoleezza Rice on Monday, the two countries issued a joint statement welcoming the formation of the new Lebanese government and its intention to hold a free and just election.
The statement stressed that the new government should spread its control over all Lebanese territories, but stopped short of pointing out Hizb Allah.
Lebanese journalist Ibrahim Awad told Aljazeera from Beirut the French have been shifting their stand in recent weeks.
He said France first called for the disarming of the resistance group Hizb Allah, but later issued another statement saying Paris understood the situation and the issue should be a pure Lebanese one.
Awad felt the French position was inconsistent.
"When France says the Lebanese government should extend its sovereignty to all Lebanese territories, it hints at southern Lebanon, where Hizb Allah is based."
Awad said: "All American demands focus now on deploying government troops in southern Lebanon. However, Lebanon has always rejected this issue under the justification that troops cannot be deployed in areas close to, or face to face with, the enemy [Israel]."
Separately, Aljazeera's correspondent in Lebanon reported on Tuesday that the Popular Front for the Liberation of Palestine-General Command had evacuated military sites in the Bekaa area.
Earlier, Lebanese Prime Minister Najib Miqati was reported as saying some Syrian soldiers were still based in the Dair al-Ashair area in Lebanon.
Miqati says some Syrian soldiers
are still based on Lebanese soil
Awad said he spoke to Miqati on Tuesday, and that the prime minister's announcement had been curtailed.
"Miqati has said that that there is a shared territory between Syria and Lebanon, and it needs to be clarified. Miqati will go to Syria on Wednesday to discuss this issue," the Lebanese journalist said.
Miqati told Awad Syria, which said last week it had completed its withdrawal from all of Lebanon, would not find it difficult to withdraw from a small area. "It is a shared territory, which is Dair al-Ashair area," Awad said.
A military source also told Awad these troops did not come from Lebanon, but from Syria.
"I believe Miqati will correct all these issues," Awad said.