Washington (CNN) -- The United States is moving toward issuing an explicit call for Syrian President Bashar al-Assad to step down, U.S. government sources told CNN Tuesday.

The move is expected to be announced in coming days after U.S. officials consult with the United Nations Security Council, the sources said.

The question of whether to call for al-Assad to step down has been under discussion over the past few weeks, the sources said.

Officials described the White House as being more eager to make the announcement while the State Department is being more cautious about the ramifications should al-Assad not heed the call.

In addition, the Security Council is expected Wednesday to follow up on last week's presidential statement, which condemned the Syrian government for violence against peaceful protesters and called for an immediate end to violence by all parties.

But no immediate escalation of that statement is expected, since Russia and China -- whose representatives usually feel it is not the Security Council's role to get involved in what they describe as matters of member countries' internal affairs -- would be unlikely to agree.

Instead, the new package would likely impose new Treasury Department sanctions on family members and business and government officials linked to the regime, said a government official involved in the deliberations who was unable to speak for attribution.

"Treasury is preparing to announce additional sanctions this week targeting major elements of Syria's financial and commercial infrastructure that are providing critical support to the regime," the official said.

In addition, there would be new steps taken to further isolate Syria from the international community, the sources said.