Senate Republicans have indicated they are willing to negotiate with Democrats on subsidies to the Affordable Care Act (ACA), known as Obamacare, but are demanding stricter abortion rules in health insurance plans.

Senate Republican Leader John Thune outlined his party's negotiating position to the press before the Senate passed a bill to reopen the government on Monday, according to NBC News.

Thune's remarks set the stage for the next partisan battle over the expiration of health subsidies, which were the main sticking point in passing a federal budget bill to end the longest government shutdown in history.

If the subsidies are not extended before the end of the year, some people insured under Obamacare could see their bills increase by thousands of dollars a month, raising concerns that millions will choose not to have health insurance.

Senate Majority Leader John Thune, a Republican from South Dakota, said an extension will be negotiated once the government reopens.

Thune added that one condition will be the enforcement of stricter rules regarding the Hyde Amendment, which prohibits the use of federal funds to finance abortions.

Senator Ron Wyden, a Democrat from Oregon, said in his speech before The Senate floor noted that the Affordable Care Act, also known as Obamacare, already prohibits the use of public funds for abortions. However, according to NBC News, Republicans intend to prevent states from allowing access to abortions through the Affordable Care Act marketplaces, using state funds or other resources.