Karami, who had resigned amid a storm of anti-Syrian protests in Beirut, said his new mission was to form a national unity government to save Lebanon from destruction.
His previous cabinet was packed with pro-Syrian ministers.
"The only way to confront all the difficulties facing the nation is a government of national unity," Karami said.
"If there is any procrastination in responding to this invitation, it means we're heading to destruction," he added.
President Emile Lahud formally asked Karami to pick a new cabinet a day after parliament, where Syria's allies have a majority, nominated him for the premiership.
It was not clear whether any opposition politicians, who had said they wanted a cabinet excluding candidates in general elections due in May, would join a unity government.
They also want a full Syrian pullout, the sacking of pro-Syrian security chiefs and an international inquiry into last month's killing of former Prime Minister Rafiq al-Hariri.
"Our main concern is not forming a government but saving the country"
Lebanese prime minister
An MP loyal to al-Hariri said her bloc would remain in opposition. "We will not take part in any government before our demands are met," Ghenwa Jallul said.
After meeting with Lahud, Karami said: "We'll continue to extend our arms to them (the opposition) and wait for them.
"Our main concern is not forming a government but saving the country," he added.
Al-Hariri's assassination in a bomb blast on 14 February has plunged Lebanon into political turmoil and dramatically increased local and international pressure on Syria to remove its troops and intelligence agents from Lebanon.
US President George Bush has demanded that Syria withdraw fully before the elections and end the "heavy-handed" influence of Syrian intelligence in Lebanon.
Lahud (L) has officially appointed
Karami as prime minister
Washington said Syria should not influence the shape of a new Lebanese government, expected to last only two months.
"This new government should reflect the will of the Lebanese people, not of Damascus," said US State Department spokeswoman Darla Jordan.
"There should be no further attempt by the governments of Syria and Lebanon to intimidate or sideline the Lebanese opposition in the run-up to parliamentary elections," she added.
Syrian President Bashar al-Assad has announced plans for a two-phase withdrawal of the 14,000-strong Syrian garrison in Lebanon.
Troops have been moving eastwards this week, with many of them crossing into Syria, witnesses and security sources say.
"This new government should reflect the will of the Lebanese people, not of Damascus"
Darla Jordan, spokeswoman for US State Department
Karami had become prime minister in October, replacing political rival al-Hariri who resigned over differences with Lahud. Karami resigned two weeks after his predecessor's death, saying he could not "carry the weight of al-Hariri's blood".
Al-Hariri's death sparked a wave of anti-Syrian street protests by Maronite Christians, Druze and Sunni Muslims.
But larger crowds supporting Syria's role turned out for a Beirut rally organised by Syrian-backed Hizb Allah on Tuesday and a march in Damascus on Wednesday.
The rival rallies have revealed deep rifts among the Lebanese over Syria's role and the future of Hizb Allah, the country's last openly armed group.