The number of District residents who have died from exposure to the cold this winter has reached 13 -- more than twice the number most recently reported -- in one of the most severe outbreaks of hypothermia deaths here this decade, city officials reported yesterday.

Seven of the victims were homeless, according to the D.C. medical examiner's office. Advocates for the homeless, however, estimated that 10 were homeless and criticized the city for failing to provide adequate shelter for the estimated 5,000 to 7,000 homeless here.

M. Jerome Woods, director of the Department of Human Services, said he is unable to explain the rise in deaths but defended the city's response to the homelessness problem, saying that District shelters have been able to accommodate everyone seeking protection.

"There are people who say that beds are not available. I challenge that," Woods said in an interview yesterday. "The city is doing the best it can with the resources it has."

Woods' comments came as Mitch Snyder, an advocate for the homeless, was preparing to do battle once again with the District government, in this instance over the right of his group to claim the bodies of the homeless dead whose families or friends do not step forward to bury them.

Snyder's organization, the Community for Creative Non-Violence, has scheduled a "funeral" for today at Western Plaza in front of the District Building for two of the homeless persons who died last month from exposure to the cold. Members of the group said the funeral would involve a procession behind closed coffins, a silent vigil and prayers led by an Episcopal minister.

However, Carol Fennelly of CCNV said that when she went to the District medical examiner's office yesterday to pick up the bodies, she was told that Woods' office would not authorize their release.

Fennelly said the refusal contradicts District policy, set after a court battle in 1980, to allow CCNV to collect the bodies of the dead if after 30 days no family members or friends had stepped forward. She said that CCNV has picked up for cremation more than 40 bodies for the past eight years in its capacity as "friend" of the homeless.

Woods said yesterday that the District would continue to honor this policy in the future, but would refuse to release the bodies for the funeral, lashing out at Snyder for using the dead to create what he called a "public spectacle."

"I find it repulsive, indecent and a lack of respect" for the dead, Woods said. "I'm opposed to it, as is the city administrator," Carol B. Thompson. Woods added he "has no intention to release {the bodies} unless ordered by a court."

Last night, lawyers for CCNV were preparing to file suit this morning in D.C. Superior Court, seeking to force the District to turn over the bodies, Snyder said.

He disputed Woods' characterization of the event planned for this afternoon and said the bodies "are being given a very dignified . . . farewell," as part of an effort to remind the public that the homeless are "all of our responsibility."

"If anything is tasteless, it's the response of the Department of Human Services" to the plight of the homeless, Snyder said. "They're embarrassed by the fact that they haven't done the job this winter because 10 people have died."

Synder was referring to CCNV's claim that 10 of the 13 people who died from hypothermia were homeless, not seven as asserted by the District medical examiner's office. CCNV members attributed the discrepancy to differences in the method of categorizing who is homeless.

District officials would not release the names of all 13 victims, although some of the names have already been made public. Previously only five cases had been reported by the news media.

The two most recent reported deaths from hypothermia were an unidentified man found last weekend in a Georgetown alley and another unidentified man found in the 300 block of 12th Street NW.

Of the remaining victims, Fennelly said that CCNV has identified five it believes were homeless: Granville Cato, discovered in an abandoned car in Southeast Washington on Jan. 8; Brian Michaeltree, found in a van in Southeast on Jan. 23; William Phillips, found in Fort Dupont Park, also on Jan. 23; John Wilkes, found in the 1100 block of Harvard Street NW on Dec. 31, and Henry Dixon, found in the 1200 block of G Street NW on Jan. 2.

City officials confirmed the deaths but would not verify whether the victims were homeless.

According to the medical examiner's office, the number of deaths from hypothermia in the District already exceeds the nine deaths during all of last winter and is second this decade only to the 14 deaths from exposure reported from December 1983 through March 1984.