Meanwhile, Washington deployed some 275 military personnel to protect its embassy in Baghdad, the first time it has publicly bolstered the mission's security.
Apart from the 41 construction workers in Mosul, there are 46 Indian nurses stranded in Tikrit — most of them are from Kerala.
Iraqi officials have insisted they are making progress in repelling the fighters, who are led by ISIL, but have continued to lose ground.
The move came as the West steps up its engagement with Iran amid rapid jihadist advances in neighbouring Iraq
The US and Iran also held an initial discussion on how the longtime foes might cooperate to ease the threat from the al-Qaida-linked militants that have swept through Iraq.
In the latest fighting on Monday, Sunni militants took control of several neighbourhoods of Tal Afar, between the now rebel-held Mosul and the Syrian border.
US officials, speaking on condition of anonymity, said Obama and his top advisers had not yet decided on a specific package of political demands to be presented to the Iraqi prime minister.
Obama, who was being presented with recommendations from his top national security advisers has made US action contingent on Iraqi PM taking steps to broaden his Shi'ite-dominated government
In all, there are 46 Indian nurses stranded in Tikrit - most of them from Kerala - and 41 construction workers are in Mosul, the embassy said.
These interruptions appear to coincide with military operations, amid concerns that ISIL forces are using Internet websites to coordinate their attacks
The US condemned a massacre in which ISIL militants appear to have killed scores of soldiers around the conflict-hit city of Tikrit
The prime minister has made major mistakes when it comes to security, for which he is directly responsible as commander-in-chief of the armed forces and acting defence and interior minister
Captions on the photos showing the soldiers after they were shot say "hundreds have been liquidated," but the total could not immediately be verified.
The Taliban's main stronghold is in the North Waziristan tribal district, where the Pakistan military began its offensive on Sunday night.
Thus far, to be precise till the midnight of 15 June, the Ministry of External Affairs has not come up with its take on the Iraq situation which has serious repercussions for India.
The Islamic militants who overran cities and towns in Iraq last week posted graphic photos that appeared to show their gunmen massacring scores of captured Iraqi soldiers
It could also redesign Middle Eastern national boundaries set nearly a century ago after the fall of the Ottoman empire, and lead to a forging of new regional alliances.
Shi'ite Muslim Iran has been alarmed by the seizure this week of several major northern Iraqi towns by Sunni Islamist insurgent forces and their sweep southward to within an hour's drive of Baghdad, and not far from the Iranian border.
Baghdad does not appear to be in imminent danger of a similar assault, although Sunni insurgents have stepped up car bombings and suicide attacks in the capital recently.
The meeting came soon after Obama told reporters that he is considering all options in Iraq as it has a stake in making sure that jihadists do not get a permanent foothold there and in Syria