WARSAW, Poland - Poland's conservative ruling Law and Justice party capitalized on its popular social spending policies to do even better at the ballot box than when it swept to power four years ago, according to nearly complete results reported Monday.

If confirmed, the results from Sunday's general election would be the strongest showing for a single Polish party in a parliamentary election in 30 years, since Poland threw off communism to establish democracy.

Law and Justice won just under 44% of Sunday's vote, up from 38% in 2015, according to results reported by the state electoral commission based on 99.5% of the votes. Under the Polish system for seat distribution, the party will still have a majority in the 460-seat lower house of parliament, but only a few seats more than before.

The Civic Coalition, a centrist alliance built around the Civic Platform party, once led by EU leader Donald Tusk, was running second with over 27% support.

Pending results from voting abroad could still adjust the figures somewhat.

Turnout was at a record high of over 61% in a sign of how important voters on all sides considered this election.

Despite the win, Law and Justice leaders were not overly enthusiastic. The result leaves them short of the two-thirds majority that they sought to change the constitution as they reshape Poland into a modern state rooted in a conservative Roman Catholic outlook that rejects abortion and gay rights.

“We achieved a lot, but we deserve more,” party leader Jaroslaw Kaczynski declared in a victory speech late Sunday.

A political adviser to the ruling party, Andrzej Zybertowicz, said that Kaczynski had counted on a “strong advantage in parliament.”

A left-wing alliance build around the Democratic Left Alliance came in third with over 12% support, which brought the left back into parliament after having no representation there over the past four years.

The conservative agrarian Polish People's Party, in alliance with an anti-establishment party led by a rock star, Kukiz 15, got nearly 9%.

Confederation, a new far-right group that is openly anti-Semitic and homophobic, was set to enter parliament after winning 6.8% of the vote.

In the less powerful 100-seat Senate, Sunday's vote saw Law and Justice falling short of a majority. It won just under 45% support. The Civic Coalition won above 35% of the vote, the Polish People's Party had nearly 6% and the left-wing alliance captured just over 2%.

Law and Justice, which has governed Poland since 2015, is popular both for its social conservatism and generous social spending, including a program that gives families a monthly stipend of 500 zlotys ($125) for each child. It ran a campaign that highlighted its social programs and vowed to defend traditional Roman Catholic values.

In the past, Kaczynski has said he wants a new constitution to “guarantee true democracy” and limit legal protections for lawmakers, judges and prosecutors. Critics fear that would amount to a power grab, given the party's track record on the judiciary and the media.

According to the European Union, the ruling party's overhaul of Poland's courts and public prosecution over the past four years has eroded the country's judicial independence.

The party also used public media to promote its successes and to cast a poor light on the opposition. Public media programing, in many cases, depicted the LGBT rights movement as a dire threat to Poland, echoing the rhetoric of members of the ruling party, Confederation and the Catholic Church.

The Organization for Security and Cooperation in Europe, which monitored the campaign, said “clear media bias” and intolerant rhetoric detracted from an election that was otherwise well-run.

“These elections were well-organized ahead of the vote, but while voters stepping into the polling booth had numerous options available to them, their ability to make an informed choice was undermined by a lack of impartiality in the media, especially the public broadcaster,” said Jan Petersen, who headed the election observation mission.

He added that: “The use of discriminatory rhetoric by a number of leading political figures is of serious concern in a democratic society.”

Monika Scislowska contributed to this report.