By Stephanie Nebehay

GENEVA (Reuters) - Yemen is "crumbling" under a deepening humanitarian crisis after months of civil war, the International Committee of the Red Cross said on Tuesday, and a U.N. investigator said sieges imposed by combatants were causing starvation.

ICRC President Peter Maurer, ending a three-day visit to the Arabian Peninsula country, called for free access to deliver life-saving food, water and medicines, while urging the warring parties to work toward a negotiated solution.

"The humanitarian situation is nothing short of catastrophic. Every family in Yemen has been affected by this conflict," Maurer said in a statement.

Some 4,345 people have been killed and 22,110 injured since March 19, the World Health Organization said on Tuesday, citing figures from Yemeni health care facilities.

A political crisis descended into civil war in March when Iranian-allied Houthi forces who had seized the capital Sanaa advanced south toward the main port of Aden, forcing President Abd-Rabbu Mansour Hadi to flee to Saudi Arabia.

A Saudi-led Arab military coalition began a bombing campaign against the Houthis on March 26 to restore Hadi and fend off what they see as Iranian influence. Houthi forces have since been pushed back on several fronts.

Intense fighting and import restrictions have severely impaired health care, Maurer said.

"Medicines can't get in so patient care is falling apart. Fuel shortages mean equipment doesn't work. This cannot go on. Yemen is crumbling. As a matter of urgency, there must be free movement of goods into and across the country ... Much more needs to be done."

Nearly 25 percent of health facilities are not functioning or only partially, WHO spokesman Tarik Jasarevic said.

Health workers have fled, creating gaps in providing primary medical treatment and war surgery. "Shortages of power and fuel have resulted in the closure of intensive care units and operation rooms in almost all hospitals," he said.

Hilal Elver, United Nations special rapporteur on the right to food, said 12.9 million people in Yemen lacked basic food supplies and 850,000 children faced acute malnutrition.

"Sieges in a number of governorates, including Aden, Al Dhali, Lahj and Taiz, have been preventing staple food items, such as wheat, from reaching the civilian population, while air strikes have reportedly targeted local markets and trucks laden with food items," Elver said in a statement.

She said the "deliberate starvation of civilians" caught in armed conflict might constitute a war crime.

(Editing by Mark Heinrich)