Coalition-building talks between the two parties, which won parliamentary elections four weeks ago, stalled in the run-up to Sunday's presidential run-off between their leaders.
Kaczynski's Law and Justice party and the Civic Platform, led by his presidential rival Donald Tusk, have common roots in the pro-democracy Solidarity movement but differ widely on economic programmes for the European Union newcomer.
Coming to a compromise may not be easy, say analysts, because the presidential race underlined deep differences between the parties on how far Poland should go with market reforms and how much welfare it can afford.
"I want to call ... for us to quickly conclude work on the government. I will approach Donald Tusk, who fought superbly in this campaign," Kaczynski told supporters after exit polls showed him with a 5- to 7-point lead over Tusk.
Prime minister-designate Kazimierz Marcinkiewicz reiterated that the coalition should be formed by the end of next week, but both camps say talks are likely to be difficult.
Donald Tusk was offered the post
of parliamentary speaker
The conservatives say election results showed that Poles were in no mood for further reforms after 16 years of often painful post-communist changes.
Kaczynski adopted a populist tone in the campaign, branding Tusk a "dangerous liberal" whose reforms would hurt the poor.
"Society has made a decision and this should be a signal for the government," Law and Justice leader Jaroslaw Kaczynski, Lech's identical twin, told private television channel TVN24.
In a goodwill gesture towards his defeated rival, Kaczynski offered Tusk the post of parliamentary speaker, a prestigious role that wields considerable power.
Tusk made no comment on the formation of the government, but his close associate Hanna Gronkiewicz-Waltz told Reuters her party may opt out of joining the government if its reform plans were ignored.
"We gave them our conditions. If they are not met, we will not take joint responsibility for the country," she said.