Okamura, 53, has faced criticism as head of the Freedom and Direct Democracy party (SPD), which has campaigned against European Union membership.
The SPD is a partner of Germany's far-right Alternative for Germany in the European Parliament.
Opposition parties have said his views are incompatible with holding one of the highest positions in Czech politics.
"I understand that I am not everyone's candidate, but I promise that if I receive confidence and am elected, I will be an impartial chairman for everyone," Okamura said during a more than six-hour debate.
Babis aims to form a government with Okamura's SPD and the right-wing Motorists party by mid-December.
The trio have finalised a government agenda that is likely to lead to higher fiscal spending, reduced support for Ukraine's fight against Russia's invasion, and stronger opposition to EU migration and climate policies than under Fiala's cabinet.
Okamura has strongly criticised aid for Ukraine and has called for a halt in benefits paid to hundreds of thousands of Ukrainian refugees settled in the Czech Republic. The SPD has called for them to return home.
However, the new coalition has explicitly ruled out in its programme any referendums on the Czech Republic's membership of NATO and EU, something previously sought by the SPD.
Czech President Petr Pavel has tasked Babis with forming the new government but has not yet appointed him as prime minister.
The two men meet next week for an update on government-building talks. Pavel has said he would protest against government nominees who could question the country's EU and NATO commitments.
(Reporting by Jan Lopatka and Jason HovetEditing by Gareth Jones)