"Let's talk, let's deal with this question, let's take risks, you and us. We need to sit around the same table and negotiate, government to government," he said.
Sanchez, who secured the backing of an unlikely alliance of mainstream Socialists, hard-leftists and Catalan and Basque nationalists to bring down Rajoy, has the slimmest parliamentary majority since the birth of Spanish democracy in 1975.
His Socialists hold just 84 seats in the 350-member assembly, which could make any bold move on the economic or political front - including on Catalonia - difficult.
He has already said he would stick to the 2018 budget crafted by Rajoy's conservatives.