Prime Minister Abiy Ahmed has called the military offensive a “law-enforcement operation”.
Hundreds of people have reportedly been killed and thousands have been forced from their homes.
Aid groups fear the conflict could trigger a humanitarian crisis and destabilise the Horn of Africa region.
In a statement released on Wednesday morning, Mr Abiy said when it came to help from outside “the international community should stand by until the government of Ethiopia submits its requests for assistance”.
On Tuesday, a UN Security Council meeting to discuss the fighting in Tigray ended without a statement, according to AFP news agency, with African countries reportedly requesting more time to allow for diplomatic efforts by the African Union to continue.
Meanwhile, the EU foreign policy chief Josep Borrell met with Ethiopia’s foreign minister to discuss the conflict.
“I expressed my great concern regarding increasing ethnic-targeted violence, numerous casualties and violations of human rights and of international humanitarian law,” Mr Borrell said after their Tuesday meeting.
On Sunday, Mr Abiy issued a 72-hour ultimatum to Tigray’s forces, telling them to surrender as they were “at a point of no return”.
But Tigray’s forces have vowed to keep fighting, with their leader Debretsion Gebremichael saying they are “ready to die in defence of our right to administer our region”.
Meanwhile, Ethiopia’s state-appointed Human Rights Commission has accused a youth group from the Tigray region of being behind a massacre earlier this month in which it says more than 600 civilians were killed.
The commission says the group stabbed, bludgeoned and burned to death non-Tigrayan residents of the town of Mai-Kadra with the collusion of local forces.
Human rights group Amnesty International first highlighted reports of a massacre in Mai-Kadra but was unable to confirm who was behind it, or exactly how many died.
The Tigray People’s Liberation Front (TPLF), a political party which controls Tigray, denied involvement, and called for an independent international investigation into the killings.
The conflict started after Ethiopia’s central government accused the TPLF of holding an illegal election and attacking a military base to steal weapons.
In response, Mr Abiy – a former Nobel Peace Prize winner – ordered a military offensive against forces in Tigray, accusing them of treason.
The TPLF sees the central government as illegitimate, arguing Mr Abiy does not have a mandate to lead the country after postponing national elections because of coronavirus.