Sudan's PM visits Ethiopia amid refugee crisis
It was the first visit by a foreign leader since fighting broke out in Ethiopia's Tigray region on November 4, creating a humanitarian crisis.
Thousands have been killed, according to the International Crisis Group, and just over 50,000 people have fled to Sudan since Abiy ordered troops into Tigray to to confront the region's dissident ruling party.
Abiy, winner of last year's Nobel Peace Prize, said Hamdok expressed support for the offensive against the Tigray People's Liberation Front (TPLF) during face-to-face talks.
"The Sudanese side reiterated their solidarity with the government of Ethiopia in the law enforcement operations it has been undertaking," said a statement from Abiy's office.
Hamdok, who is in Addis Ababa for two days, also recalled the support Abiy had extended to Sudan, it added.
Accompanied by a large security delegation, Hamdok said he looked forward to "productive discussions on political, humanitarian and security matters".
The Sudanese premier had urged Abiy to engage in negotiations with the TPLF when fighting broke out six weeks ago, and encouraged African mediation to resolve the conflict as it threatened to drag in the wider region.
Abiy has resisted international pressure to end fighting and accept mediation, saying TPLF leaders needed to be disarmed and apprehended.
On November 28 he declared the conflict over, saying the army had captured the regional capital Mekele, and has dismissed reports of ongoing clashes as "sporadic gunfire" not indicative of major combat.
Over the weekend AFP journalists saw trucks of soldiers heading north and ambulances remain a common sight in southern Tigray and northern Amhara regions.
Tens of thousands of refugees have crossed the border westward into one of the most impoverished regions of Sudan, itself one of the world's poorest countries.
The influx comes with Sudan undergoing a fragile political transition since last year's ouster of president Omar al-Bashir and facing an economic crisis which has been especially felt in the eastern states of Gedaref and Kassala - the main arrival points for refugees escaping Tigray.
Around 170 refugees crossed into Sudan from Tigray on Saturday, according to the UN refugee agency UNHCR, compared to 1,100 on December 3.
Agencies contributed to this report.