Nicola Sturgeon declared the SNP has "made history" by winning a third term in government at Holyrood but the party failed to reach a majority.
The Scottish Conservatives had their best ever result, securing 31 MSPs, while Labour suffered its worst result since devolution with 24 MSPs.
Prime Minister David Cameron has called Scottish First Minister Nicola Sturgeon to congratulate her on the SNP's election success, a Downing Street spokesman said.
The SNP claimed an historic third successive victory in the Parliamentary elections - though fell just shy of a second overall majority.
In return, Ms Sturgeon congratulated Mr Cameron on the gains made by the Conservatives, who won an all-time high of 31 seats - pushing Labour into third place.
The spokesman said the leaders discussed how they could work together on issues such as those facing the steel industry.
21-year-old Ross Greer has been elected as the youngest-ever Member of the Scottish Parliament (MSP), representing the Green Party.
Labour is facing a disastrous election night in Scotland, with the party in danger of finishing third behind the SNP and the Conservatives.