Progressive Bulgaria secured 44.7 percent of the vote, according to figures released by the country's electoral commission after 92 percent of ballots had been counted.
That puts the party on course for between 129 and 131 seats in the 240-seat National Assembly, according to independent analysts – enough to govern alone.
Its nearest rivals finished far behind.
Former prime minister Boyko Borisov's GERB party took 13.4 percent, followed closely by the pro-Western We Continue the Change–Democratic Bulgaria coalition on 13.2 percent.
Speaking after the result, Radev said he would do "everything possible" to avoid yet another early election in Bulgaria, a country that has held eight parliamentary votes since 2021, seven of them snap elections.
"This is a victory of hope over distrust, a victory of freedom over fear, and finally, if you will, a victory of morality," he told a press conference late on Sunday.
The electoral commission has four days under Bulgarian law to announce the official seat allocation, and seven days to publish the names of elected MPs.
The result is being watched closely in Brussels and Kyiv.
As president, Radev opposed military support for Ukraine and called for negotiations with Russia.
Bulgaria is a significant arms and ammunition producer, and any shift in its supply policy could have consequences for Ukraine's war effort.
He has also criticised the EU's reliance on renewable energy.
(ał/gs)
Source: PAP, IAR, Reuters