The conservatives, which are expected to approve their election programme on Monday, want to cap the corporate tax rate at about 25% from just under 30% now.
"Laschet is still a long way from the chancellor's office," the Sueddeutsche Zeitung daily said. But the poll result has brought him "much closer to it".
The CDU under new party chief Armin Laschet won between 35 and 36 percent of the vote, exit polls showed, with the anti-immigration party on between 22.5 and 23.5 percent.
Although support nationally has stagnated at around 10 to 12 percent for the AfD in recent months, in Saxony-Anhalt -- as in other former East German states -- the party has long had a strong base of support.
"I have no sign of movement in any of the candidates so far," said one CDU lawmaker who supports Soeder.
The rivals to succeed Merkel, who is stepping down after a Sept. 26 federal election, went head to head on Tuesday to win the support of lawmakers, exposing deep rifts within the parliamentary bloc.
Long-time Merkel ally Laschet took over as CDU leader in January but has since suffered a series of setback including a damaging spat with Merkel over virus containment measures.
Laschet, premier of Germany's most populous state and the self-styled Merkel continuity candidate, won 83.35% of the valid postal votes cast by 1,001 delegates.
"The CDU remains Germany's Europe party," Laschet told reporters, stressing that he wanted his leadership of the party to be marked by dialogue with its grass roots.
