A union representing 30,000 home health aides in New York City is stepping up a campaign to increase wages for its members, a message it plans to deliver at a rally today at Madison Square Garden.

The union, 1199 SEIU, is seeking better wages for 20,000 members whose contracts expired in recent months, and its leaders are threatening to strike if contracts are not secured by September.

Union officials said they want members to earn $10 an hour, up from an average of $8 an hour. They are also seeking first-time contracts for about 10,000 aides.

“At the end of the day, the people providing the care don’t get paid,” the president of 1199 SEIU, George Gresham, whose mother is a retired home health aide, said.

Home health care is one of the fastest growing occupations in New York City, and even as 1199 seeks better wages for its members, the union is working to build membership among aides who are not part of the union. “They are in need of representation,” a lawyer for 1199 who is involved in strategic planning, Kevin Finnegan, said. Aides represent “the last large area of health workers in the state that hasn’t been organized.”

The largest union contract is with Partners in Care, a subsidiary of the Visiting Nurse Service of New York, which employs 5,000 home health aides. The contract expired May 31, and last night representatives from the union and the agency were set to meet for a negotiating session. A spokesman for the Visiting Nurse Service declined to comment pending contract negotiations, but union officials said they expected to reach an agreement with the agency.

They did not rule out a strike similar to one in 2004, when 25,000 home health aides walked out. Mr. Gresham said he thought it was “inevitable” that “we may have to strike at least a couple of the agencies.”

Home health aide Lorna Selwood, 50, who earns $8.50 an hour, said she sometimes works 12-hour days for a client in the Bronx. “We deserve a lot more,” she said.