The party has won the largest number of votes in the last three elections and the only reason it did not enter government is it failed to attract coalition partners.
The National Alliance is expected to win 13 and Unity, now rebranded as New Unity, might not even meet the five-percent election threshold.
This time around, however, it could find the necessary ally in the KPV LV, a populist party led by former stage actor Artuss Kaimins, who has retained popularity with voters despite his being detained over corruption allegations in June.
"I am going to make my choice for Latvia as part of the European Union and North Atlantic Treaty Organisation, and I hope most of us will do, otherwise this election will be remembered as the Red October", he told AFP.
Polling stations in Latvia opened Saturday for a general election that could propel a populist, pro-Kremlin coalition to power as the Baltic state celebrates the centenary of its birth as an independent state.More news: Jose Mourinho could still be sacked by Manchester United
Leader of the Social Democratic Party Harmony, which is winning the parliamentary polls, has called on the Latvian president to allow its candidate Vyacheslav Dombrovsky to form a new cabinet of ministers.
The center-left Socialist party, commonly known as Harmony, received almost 20 percent of the vote after ballots from 575 polling stations were counted.
The result means a confirmation of the European Union and North Atlantic Treaty Organisation member's role as a bulwark against Russian Federation in the increasingly hostile relationship between the West and President Vladimir Putin.
According to the latest polls the ruling coalition of the Union of Greens and Farmers, the National Alliance and the Unity party looks to be well short of forming a majority government.
It has a sizable ethnic-Russian minority of around 25 percent, a legacy of almost 50 years of Soviet occupation that ended in 1991, when the nation regained its independence. Some 1.5 million Latvians were eligible to vote. "The parliament of Latvia and our country will be a good example for Europe, a smart nation, and a civil society".More news: Liveblog: Google’s Pixel 3 launch event at 11am ET Tuesday, October 9
We expect change and need more patience of the government with 16 competing parties.
Relations between Russian Federation and Latvia have been frayed by Russia's 2014 annexation of the Crimea Peninsula from Ukraine and its support for separatists in eastern Ukraine.
According to the Baltic News Service, Latvian security police were investigating 70 suspected cases of voting fraud. Sunday's results give the party 23 seats, one less than in the last election.
But Harmony's pro-Russian stance is still an issue.More news: Why Arsenal’s 5-1 win is "deceitful", Lacazette