Griffiths has said he hopes to host talks by the end of the year.
The Saudi-led Arab coalition intervened in Yemen's conflict in March 2015 in a bid to roll back the Shiite Houthi rebels and reinstate Yemeni President Abdu-Rabbu Mansour Hadi.
The U.S. State Department said on Sunday that Secretary of State Mike Pompeo had a phone conversation with Saudi Crown Prince Mohammed bin Salman on Khashoggi's death.
Griffiths, said the statement, reassured the warring sides that the United Nations remained ready to re-engage the parties on a negotiated agreement for Hodeida, which would protect the port and preserve the humanitarian pipeline.
Rebel-held Hodeida was hit Monday night by what multiple sources said were two air strikes - the first targeting of the docks since government forces launched a major offensive to retake the port five months ago.
The Saudi-backed government forces vowed to continue to push forward in an attempt to seize full control over the city's strategic port, but Houthis face the offensive with stiff resistance.
Saudi-led coalition spokesman Colonel Turki al-Maliki had no immediate confirmation of the strikes but told AFP he would check.
Medics in hospitals across Hodeida province reported 111 rebels and 32 loyalist fighters killed overnight, according to a tally by AFP.
Michael Avenatti reportedly arrested on domestic violence charges
This is not the first time that Avenatti's wife has mentioned abuse. "I look forward to being fully exonerated", he said . The decision to cancel the events was made "almost immediately after the news broke", he said.
Both the Huthis and Saudi-led government camp reported outbreaks of violence elsewhere in Yemen late Tuesday.
"The Saudi-led coalition (has) agreed to the evacuation of wounded Houthis from Yemen, one of the key stumbling blocks to the UN Geneva talks in September", it added. He said three guards had been wounded.
The fighting around the city, a vital lifeline for most Yemen's population, threatens to worsen Yemen's already-dire humanitarian situation and risks the obstruction of crucial assistance to the country endangering the lives of millions of Yemenis.
There have been global outrage over the murder of US-based Saudi journalist Jamal Khashoggi, and after Democratic and Republican politicians had threatened to take action in Congress next week over the refuelling operations.
Mutawakel said Saudi Arabia's refusal to let exiled President Abed Rabbo Mansour Hadi's government maintain a presence on the ground, the blockade of air and sea ports of entry and the collapse of Yemen's currency after the closure of the country's central bank had also driven the starvation.
Why it matters: After Defense Secretary Jim Mattis announced that the United States would stop refueling Saudi and Emirati warplanes in Yemen, the deal leaves open a tiny window for UN-led peace talks in Yemen.
The United States, Britain and France - three of the main arms suppliers to Saudi Arabia - have also called for an end to almost four years of conflict, particularly in the Red Sea city of Hodeida.