President Reagan yesterday signed an emergency spending bill that keeps the government in business through midnight Tuesday, a White House spokesman said.

The bill, the third extension in a week, is a stopgap measure that maintains current funding levels for government agencies whose regular appropriations bills have not yet been approved. These include the departments of Defense, Agriculture, the Interior, Labor, Health and Human Services, Education, Transportation and the Treasury.

The extension was approved in both chambers of Congress Friday after House-Senate conferees again failed to reach agreement on a nearly $500 billion omnibus spending bill for these agencies for the next 12 months.

Federal offices are expected to open Tuesday after the Columbus Day holiday weekend, but legislators will that day have to pass the spending bill or yet another extension to avoid a repeat of Thursday's disruption in government business.

Meanwhile, administration officials said they had resolved their differences over water projects Congress has tacked onto the omnibus spending bill -- differences that on Friday had sent conflicting signals to Capitol Hill.

The White House had threatened to veto the spending bill because of several dozen water projects attached by Congress. Office of Management and Budget Director David A. Stockman had urged Reagan to issue the veto warning because the bill lacks reforms in cost-sharing and user fees sought by Reagan.

But Interior Secretary William P. Clark had suggested Friday to Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) that the president still wanted three U.S. Bureau of Reclamation projects in the bill that were budgeted for fiscal 1985.

The issue apparently was settled yesterday when White House Chief of Staff James A. Baker III wrote a letter to Clark saying the administration would "continue to support" the three water projects.

They are: Animus La Plata in Colorado; Buffalo Bill in Wyoming and Headgate Rock in Arizona.

Clark said in a letter to Baker that the cost-sharing reforms would be adhered to. Baker said Reagan continues to oppose other Army Corps of Engineers water projects in the spending bill unless the reforms in cost-sharing and user fees are incorporated.