"We are in constant contact with all the parties involved to negotiate arrangements for Hodeida that would address political, humanitarian, security concerns of all concerned parties," said Martin Griffiths in a statement.
Yemeni forces backed by a Saudi-led coalition launched the assault despite UN warnings of a "catastrophic humanitarian impact."
The Red Sea port serves as the entry point for 70 percent of Yemen's imports as the country teeters on the brink of famine.
Griffiths was in Amman following an intense round of shuttle diplomacy this week with Yemen's Huthi rebels, who control the port, Saudi Arabia and the United Arab Emirates, whose forces are backing the Hodeida offensive.
"We continue to use every opportunity to avoid military confrontation in Hodeida," said Griffiths.
He called on all sides to "exercise restraint and to give peace a chance."
Griffiths is also leading UN diplomatic efforts to resume political talks on ending the three-year conflict that has brought Yemen to its knees.
The attack on Hodeida, however, could derail that effort.
Griffiths is scheduled to brief the Security Council on a proposed roadmap for peace talks on Monday.
"The United Nations is determined to move ahead with the political process despite the recent developments," he said.
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