The District of Columbia's advisory neighborhood commissions, once threatened by a congressional cutoff of all their money, have won a promise of partial financing to maintain operations for their second year.

Rep. William H. Natcher (D-Ky.), chairman of the House District Appropriations Subcommittee, told a joint Senate-House conference committee meeting last week that his unit would agree to provide between $350,000 and $500,000 for the commission - known as ANCs - during the 1978 fiscal year.

The coferees reached no official conclusions in their attempt to resolve differences between the House and Senate versions of the District's $1.3 billion budget, with a proposed convention center as the biggest issue.

The ANC item was the one that came closest to a solution. The conferees are scheduled to meet again Monday.

The House version of the budget, recommended by Natcher's subcommittee, eliminated the entire $1 million of ANC financing sought by the city government. The action brought protests from city officials and members of many of the 36 ANCs.

The Senate, in its version of the budget, agreed to provide $500,000.

Sen. Patrick J. Leahy (D-Vt.), chairman of the Senate District Appropriations Subcommittee, urged the conferees to accept the $500,00 figure, bringing the response from Natcher. If the ANCs do no function well in the coming year, future funds could be eliminated, Leahy said.

Rep. Gunn McKay (D-Utah) voiced concern that the ANCs may evolve into a shadow government, "a monster we may have to deal with down the world."

Despite the lack of an official agreement on the ANCs, the "continuing resolution" adopted by Congress on Thursday to provide stopgap financing of the D.C. government until Oct. 31 provides for ANC funding at half of last year's level. The ANC provision was recommended by Natcher.