Details about Hammer's ongoing visit were scant, with no information available from either Prime Minister Abiy Ahmed's government or US authorities.
The United Nations' special envoy for the Horn of Africa, Hanna Serwaa Tetteh, "met the US envoy today in Addis but there are no plans for a joint mission," a UN spokesperson told AFP late Monday.
Getachew Reda, spokesman for the Tigray People's Liberation Front (TPLF) rebel group, would not confirm any plans to see Hammer.
But he told AFP in a message on Tuesday: "We are willing to meet anyone with a serious intention to resolve the war on Tigray peacefully."
In a press conference uploaded to the YouTube channel of TPLF-linked Tigrai TV late Monday, Getachew described "very intense fighting" under way and said the rebels were resisting joint offensives by forces from Ethiopia and neighboring Eritrea.
The United States dispatched Hammer, its special envoy for the Horn of Africa, to Ethiopia at the weekend, after the resumption of fighting last month shattered a truce and dashed hopes of ending a humanitarian crisis triggered by the nearly two-year war.
During his previous trip to Ethiopia last month, Hammer travelled to Tigray with his EU counterpart Annette Weber, and the pair angered federal authorities by urging them to restore basic services such as electricity and communications to the stricken region.
Fighting had been concentrated around the southeastern border of Tigray, but has since spread along the region's southern border, to areas west and north of the initial clashes.
"Our forces were able to defend their positions effectively in Wag (in Amhara region, which neighbours Tigray) and are now launching a counter-offensive," said Getachew.
AFP was not able to independently verify the claims. Access to northern Ethiopia is severely restricted and Tigray has been under a communications blackout for over a year.
Addis Ababa has not responded to requests for comment.
The two sides have traded blame for starting the latest round of hostilities, with the TPLF accusing Abiy's government and Eritrea -- which backed federal forces during the war's early phase -- of launching a joint offensive against Tigray.
