BERLIN — Getting European Union leaders to agree by the end of the week on a far-reaching deal to tighten political and economic ties is looking more difficult than just a few days ago.

A senior German official says his government will not consider an alternative proposal to enforce budget discipline and save the euro that has been put forward by a top European Union official.

The senior German official, speaking on condition of anonymity, said the government of Chancellor Angela Merkel is insisting on either a substantial change to the treaty governing the 27 EU countries, or an entirely new treaty for the 17 countries that use the euro.

But Herman Van Rompuy, the president of the European Council, says an easier way to get agreement on future fiscal discipline would be to simply amend existing rules that apply to the 17 countries.

This split and others — including on whether to make automatic penalties for countries that overspend — has the potential to delay any agreeement by European leaders, who had hoped to clinch one at the end of a summit in Brussels on Friday.

It could be Christmas before everyone agrees to a new treaty, the German official said. "If several rounds of negotiations are necessary for that then we are also prepared for that."

Plans by France and Germany to save the euro through closer European unity faced a serious challenge from Britain, highliting deep divisions between the 17 EU nations that use the euro and the 10 others that don't.

British leader David Cameron is wary of losing power with the 27-nation bloc if France and Germany create a tighter club of eurozone nations with tough rules for national budgets and automatic sanctions for those who stray.

On the other hand, his government does not want to transfer any of its decision-making powers to Brussels.

Markets have neverthless rallied over the past few days on the hope that at least a tentative deal will be secured this weekend. Stocks and bonds have risen, while the borrowing rates for key countries like Italy and Spain fell to monthly lows.

Experts say those gains are based largely on hopes that the European Central Bank will eventually step up its support for weak eurozone countries.

ECB President Mario Draghi hinted in a speech last week that a commitment by euro countries to crack down on overspending could set the stage for further financial assistance from the bank.

Markets have interpreted Draghi's comments to mean that the ECB could get more aggressive in purchasing European government bonds. Those bond purchases would likely drive down interest rates, allowing debt-laden countries to cut their borrowing costs.

Earlier Wednesday, U.S. Treasury Secretary Timothy Geithner said he was very encouraged with the progress Europe is making in coming up with a plan to shore up the euro in the wake of a crippling debt crisis.

Geithner's comments to reporters followed a meeting with French Finance Minister Francois Baroin on the second day of his whirlwind trip through Europe.

"We are very encouraged with the progress that is being made," Geithner said.

Gabriele Steinhauser in Brussels contributed to this report.