Yemen urged the international community "to quickly intervene by land forces to save" the country, specifically in the cities of Aden and Taiz, according to a letter sent to the United Nations Security Council on Wednesday.
The letter from Yemen's U.N. Ambassador Khaled Alyemany, seen by Reuters, could provide legal cover for such a move.
A Saudi Arabia-led coalition launched air strikes against Houthi rebels a day after Yemen notified the 15-member Security Council in a March 24 letter that it had requested military help from Gulf Arab states.
The Houthi militia battled its way into Aden's Tawahi district on Wednesday despite Saudi-led air strikes, strengthening its hold on the city whose fate is seen as crucial to determining the country's civil war.
The letter sent to the Security Council also urged human rights groups to document "barbaric violations against a defenseless population." It accused the Houthis of killing civilians and blocking medical teams.
The fighting across Yemen killed 120 people on Wednesday, mostly civilians, including at least 40 who were trying to flee the southern port city of Aden by a boat that was struck by Houthi shells, rescue workers and witnesses said.
The Houthis and ex-army forces loyal to former president Ali Abdullah Saleh have besieged Aden for weeks in an effort to end resistance in the city where President Abd-Rabbu Mansour Hadi briefly based his government before fleeing to Saudi Arabia.
"Everyone that has committed a crime will not escape punishment and the government will employ all means to bring the Houthis and forces loyal to former President Saleh to international justice as war criminals," Alyemany wrote in the letter to the Security Council.