On Friday, however, Mr. Turner and Mr. Abbott seemed to put a momentary end to their dispute, appearing together at a news conference during which the governor handed the mayor a check for $50 million to aid the city’s recovery.

The money came not from the Rainy Day Fund but from an emergency disaster fund overseen by the governor’s office. Mr. Turner said he was rescinding his proposal to temporarily raise property taxes, because the $50 million was roughly the same amount his property-tax plan was expected to generate.

“We’re proud to be here wearing the same jersey, on the same team, working for the same constituents to make Texas better,” Mr. Abbott told Mr. Turner as the two men sat side by side in Houston City Hall.

City officials said they would use the $50 million to pay for a series of expenses, including the removal of debris. The federal government is paying for most of the debris-removal costs, but Houston’s share will be at least $25 million. In addition, officials said the city was without flood insurance for its public buildings because the damages from Harvey exceeded the $100 million limit on its policy. It will cost the city about $10 million for a new policy to cover damages from any future flooding.

“It does address some of those immediate concerns,” Mr. Turner said of the $50 million.

The meeting came after the governor was criticized for his handling of the mayor’s request to tap the Rainy Day Fund, which has $10.3 billion and is the largest of its kind in the country. A sharply worded editorial in The Houston Chronicle urged Mr. Abbott to call a special legislative session and invoked the famous “Ford to City” headline in The New York Daily News in 1975, during that city’s financial crisis.