Congo's powerful Catholic church has challenged the surprise win of opposition leader Felix Tshisekedi in the country's presidential election, saying official results do not match the outcome compiled by its 40,000 observers at all polling stations nationwide.

The church refused to name its "clear winner," but diplomats briefed on its findings said opposition leader Martin Fayulu won easily and that other election observers showed similar results.

Fayulu alleges that longtime President Joseph Kabila engineered a backroom deal with the largely untested Tshisekedi to thwart anti-corruption efforts in a country with staggering mineral wealth. He denounced the official vote results as "rigged" and called on people to "rise as one man to protect victory."

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But the country was largely calm as many Congolese appeared to accept the country's first peaceful, democratic transfer of power.

"This could be the beginning of a historic era in the (Democratic Republic of the Congo) if peace holds and finally the election results are accepted," said CBS News' Debora Patta.

Patta said the country hasn't seen a peaceful transition to power since Belgian rule ended in 1960.

Tshisekedi, who received 38 percent of the vote according to official results, had not been widely considered the leading candidate. Long in the shadow of his father, the late opposition leader Etienne, he startled Congo last year by breaking away from Fayulu -- the opposition's unity candidate -- to stand on his own.

"Nobody knows how he would be able to cope with the position of president," Patta said of Tshisekedi. "He has a tough task ahead of him."

Felix Tshisekedi gestures as he is surrounded by his wife, relatives and supporters of his UDPS party (Union for Democracy and Social Progress), a few minutes after he was declared winner. Caroline Thirion/AFP/Getty Images

Among the challenges he would face is an Ebola outbreak in the east of the country. It is the second-deadliest in history, with 335 confirmed deaths.

It also remains to be seen whether Tshisekedi has the intention or the capacity to challenge Kabila's strong hold over intelligence services, security services and key ministries in the country, CBS News' Patta said.

The delayed results, nearly two weeks after the Dec. 30 vote, came after international pressure to announce an outcome that reflected the will of the people, with the United States threatening sanctions.