The United Nations has warned that up to 250,000 people were at risk if the coalition moves ahead with an all-out offensive to take the port, which is a major entry point for commercial supplies and aid.
"I hope that there will be a way to avoid the military confrontation in Hodeida," Guterres told reporters.
"We recognise the UAE's security concerns and these need to be addressed," British Ambassador Karen Pierce told reporters ahead of the meeting. "But we are also worried about the humanitarian situation." The coalition maintains that the Red Sea port is used by Yemen's Huthi rebels to smuggle weapons.
Griffiths told the council in April that he was working on a peace plan for Yemen but that any military action risked derailing that effort.
"What we should not see is an attack on Hodeida port." More than 22 million people in Yemen are in need of aid -- 8.4 million of whom are on the brink of starvation, according to the United Nations which considers Yemen to be the world's worst humanitarian crisis.
Since 2015, Saudi Arabia has been leading a military campaign to push back the Huthis and restore the internationally recognized government to power.
The conflict has left nearly 10,000 people dead in Yemen, already the Arab world's poorest country.