The most immediate challenge facing Prime Minister Recep Tayyip Erdogan is to settle the choice of a new state president.
Parliament's rejection of Erdogan's candidate, Foreign Minister Abdullah Gul, is what precipitated the early elections. The secularist opposition distrusts Gul, a devout Muslim whose wife wears an Islamic head scarf in public -- which is seen by some Turks as a symbol of Islamic militancy.
To simply resubmit Gul's name could lead to a new deadlock, as the AK still lacks the two-thirds majority needed to push the nomination through.
"One of the biggest reasons the AK party was returned to power was simply the fact that it delivered so well on the economy," said Amberin Zaman of "The Economist."
Erdogan hinted at compromise when he told journalists in Ankara that he believes the question of the president will be resolved "without causing tensions." At the same time, he suggested that Gul himself must make the decision on whether or not to stand.
Amberin Zaman, the Turkey correspondent for "The Economist" magazine, said Erdogan will have problems, particularly with Turkey's secular estabishment, if Gul insists on standing again.
"One of [Erdogan's] first messages after declaring victory was to say to people who did not vote for them: 'We acknowledge your concerns and we don't want to raise tensions, we want to address your concerns as well,'" Zaman said. "So what sort of message would he send if he renominates Mr. Gul? He would be basically saying he was not sincere."
Momentum Toward Europe
The second challenge facing the prime minister is to continue with legal and administrative reforms needed to equip Turkey for European Union membership, and also to keep the economy rolling forward.
Brussels has already signalled that it wants Ankara to regain lost momentum in its membership bid. In remarks to journalists on July 23, EU Enlargement Commissioner Olli Rehn said the bloc expects a new Turkish government to be formed quickly. "It is essential that the new government will relaunch the legal and economic reforms with full determination and concrete results," Rehn said.
As for the economy, correspondent Zaman suggests that the healthy growth rate -- currently 7 percent per annum -- is a major reason for the AK party's near-landslide win in the weekend elections.
"One of the biggest reasons the AK party was returned to power was simply the fact that it delivered so well on the economy," she said. "The average Turk has seen his life improve, particularly the poorer Turks. The AK party has done a lot to help these people. If you go to rural areas, many people will tell you that."
The Kurdish Conflict
A third major challenge facing Erdogan in the longer perspective is the question of the Kurdish insurgency in southeast Turkey.
For the first time in some years, the new parliament includes Kurdish deputies, 27 in all. Zaman sees a heavy responsibility resting on these legislators. She says their job is to persuade the nation that the Kurdish conflict can be settled by negotiation.
The situation is complicated by the emergence of the autonomous Kurdish region in northern Iraq, which many Turks see as a spur to Turkish Kurd demands for eventual independence.
Turkish troops are massed along the Iraqi border, ready for a possible incursion in pursuit of guerrillas based there. But Erdogan appears not to favor military action, considering that the Turkish military has already made 29 incursions onto Iraqi territory since the 1990s, without dislodging the guerrillas.