The Taliban, which has fought a bloody war with US and Nato forces since being pushed from power in 2001, said that Obama, should pull his troops out of the country and let Afghans decide their own fate.
"We have no problem with Obama ... [but] he must learn lessons from Bush and before that the Soviets," Yousuf Ahmadi, a spokesman for the movement told the AFP news agency.
"We are a free nation, as they are. They have come here and they want to decide our fate for us. This is not possible. We Afghans want to decide our fate ourselves."
The focus on foreign affairs comes after the first African-American president spoke to "all other peoples and governments who are watching" in his inauguration speech on Tuesday.
"America is a friend of each nation ... who seeks a future of peace and dignity," he said, promising "mutual respect" with the Muslim world.
The 44th president's team is still being formed but is expected to include Hillary Clinton, his former rival for the Democratic presidential nomination, as secretary of state, after a vote in congress on Wednesday.
George Mitchell, who was involved in the Israeli-Palestinian conflict under Bill Clinton, the former US president, is expected to be nominated as Obama's Middle East envoy.
Alistair Crooke, a former EU adviser on the Middle East, told Al Jazeera that the 75-year-old former senator, who is known for his peacemaking efforts in Northern Ireland, was "different" from other envoys.
"He is very, very patient and he is extremely good at understanding it is a choreography of building confidence that is actually the main part of building a peace process," he said.
Obama is under pressure to focus on the Middle East as Israeli forces withdraw from the Gaza Strip after an offensive that has left more than 1,300 Palestinians dead, nearly a third of them children, and more than 5,000 injured.
Thirteen Israelis, including three civilians, died in the 22-day war.
"I think the new administration has shown all the signs of being very cautious, the last thing they wanted was to dive into the Palestinian-Israeli conflict at the first point," Crooke told Al Jazeera.
Obama has signalled his intention to break from some of his predecessor's more controversial policies.
|Judges at Guantanamo Bay will rule on Obama's suspension of tribunals [File: EPA]
Shortly after his inauguration on Tuesday, Obama requested a 120-day suspension of military tribunals at the US detention centre at Guantanamo Bay.
Judges at the facility at the US naval base in Cuba are expected to rule on the request later on Wednesday.
Obama has asked for proceedings to be halted in cases pending against 21 men, including a case against five people accused of plotting the September 11, 2001 aeroplane attacks on the US.
"The president has verbally ordered a suspension to the tribunals at Guantanamo Bay," Al Jazeera's Monica Villamizar reported from the facility.
"It's not an executive order closing Guantanamo Bay, but a halt to the trials for 120 days."
Prior to his inauguration, Obama had vowed to close down the detention centre.
Obama's economic aides were also likely to have a busy first day as they begin the task of tackling a worsening recession and push an $825bn economic stimulus package through congress.
In a sign of the struggle ahead, shares in the United States and Asia slipped despite the "feel-good factor" of Obama's inauguration.
Before begining work on Wednesday, Obama will attend a prayer service at Washington's National Cathedral.