Hundreds of voters voted Tuesday in Sanaa's old town section to replace Yemen's longtime ruler, Ali Abdullah Saleh, in an election marred by sporadic violence.

While the election was short on candidates -- the only person on the ballot was Vice President Abdurabu Mansur Hadi, who became acting president in November as the result of a power transfer brokered by the Gulf Cooperation Council after months of protests -- it appeared to be long on hope.

"It's the first time people in Yemen are electing somebody on their own, without being influenced by political parties," said Mohammed al-Rowdy, a voter who works with the Interior Ministry. "This is a people's election. That's why we are optimistic things will get better."

In a statement, U.S. Secretary of State Hillary Clinton congratulated the people of Yemen "on today's successful presidential election," calling it "another important step forward in their democratic transition process."

But she said that more work remains. "As part of the GCC Initiative, Yemenis will convene a National Dialogue Conference to address critical issues of national unity and the fundamental structure of Yemeni government and society, while taking steps to address urgent economic, social, and humanitarian challenges," she said. "The United States, along with its partners in the international community, will continue to support Yemen as it works to implement these reforms and confront these challenges so that all Yemenis will have the opportunity to realize their potential."

Officials in Sanaa described a successful effort Tuesday, but conditions in the southern port city of Aden were different. Four people were killed in clashes between gunmen and security forces, two senior security officials in the city said.

Another 14 people were injured and were treated at a hospital, security officials said.

In the port city of Mukalla, southwest of Sanaa on the Gulf of Aden, a soldier was killed Tuesday and four were wounded when polling centers were stormed, Yemen's official news network SABA reported, citing an official source.

"Gunmen have ambushed the soldiers, as they were removing stones from a street in Ghuaizi area in Mukalla," the agency reported.

"Outlaws" were blamed for breaking into polling centers in two districts of Hadramout, the source said.

And a sniper killed a member of the security forces at a polling station, said members of the Supreme Commission for Elections and Referendum.

But there were no signs of such problems in Sanaa's At Altabari school -- one of the oldest in the capital. Voters left with ink on their fingers and thumbs, proof of their participation in a historic election that signifies the formal end of Saleh's 33-year reign.

"I was particularly very impressed in seeing the women turning out," said Michele Cervone d'Urso, European Union ambassador to Yemen, who was observing the polling station. "The women are the key for this county, for sedating this country," he said in reference to the need to calm conditions there. "They have to be recognized as a key part of society."

Security around Sanaa and elsewhere was tight Tuesday.

Around the capital, posters of Hadi have replaced posters of Saleh. "A New President for a New Yemen," read a banner hanging from Change Square, which was the epicenter of the anti-government movement last year.

Some who took part in the protests said they were not particularly excited about Tuesday's vote.

"Maybe you can call them elections," Nadia Abdullah said. "But for me, elections should have more than one candidate."

Still, Abdullah said she would stand by Hadi as long as he made good on his promises.

"If he goes through with it, we will stand hand in hand with him," she said. "If he doesn't, or if we see a lot of game-playing between him and the government, I believe the youth will remain in the squares. They would say, 'Leave,' as they did to Ali Abdullah Saleh."

Abullah al-Saidi, 27, an accountant volunteering as an election observer, told CNN he voted against Hadi by putting an "X" next to the name instead of a check. He said he believes many people do not realize they have the option of voting against the vice president.

"He is old school -- I don't believe he will change a lot," al-Saidi said of Hadi.

D'Urso said the elections are not "simply for vice president Hadi. These are the elections for process, a different Yemen. And you can see Yemenis want to move to a different type of society, one of co-existence and tolerance. It's not going to be easy. I think transition in this country will probably take a generation, but I think we are moving forward, and we have kicked off in the right way today, at least here in Sanaa."

Human Rights Watch called on Hadi to make changes without delay.

"Yemen's potentially historic transition will be off to shaky start unless Hadi makes an immediate break with the abuses of the past," said Letta Tayler, HRW's Yemen researcher. "Yemen's new leader needs to move decisively to usher in promised reforms that uphold human rights and the rule of law."

The 65-year-old Hadi is a British-, Egyptian- and Soviet-trained army officer, recently promoted to field marshal. He has been vice president since 1994 and is running for a two-year term as president on pledges of improving security and creating jobs.