Leadsom cited the purdah period that comes with the calling of a general election as the reason behind the application for the extension, but insisted that the Government does have a plan ready.
He said: "This is a public health issue and not a political issue".
The hearing has been listed for Thursday morning.
The courts had given ministers until 16:00 on Monday to set out draft measures to combat illegal levels of nitrogen dioxide (NO2) pollution.
The Government has been accused of "pure political expediency" in seeking to delay publishing plans to tackle air pollution until after the general election.More news: Obama makes no mention of Trump in first major post-presidential appearance
The ruling followed a legal challenge by the environmental law firm Client Earth which claimed Defra had taken "minimum" steps in order to comply with the European Union directive on nitrogen dioxide emissions (NOx). It asked judges to allow them to breach the Monday deadline to "comply with pre-election propriety rules".
LONDON, April 24 The British government intends to publish a draft copy of its report on tackling air pollution by the end of June, ahead of publication of a final report in September, environment minister Andrea Leadsom said on Monday.
ClientEarth, the group of environmental lawyers that has successfully challenged the government twice over air pollution, described the government's move as "unacceptable".
Nitrogen dioxide emissions from diesel traffic cause 23,500 of the 40,000 premature deaths from air pollution each year, according to figures from the Department for Environment, Food and Rural Affairs (Defra).
"This is a matter for the court to decide once the Government has made its arguments because it is the Government which has not met, and instead seeks to extend, the court's deadline for the clean air plan to clean up our air".More news: UC Berkeley ReInvites Ann Coulter, But There's a Catch
Last week figures obtained by Labour showed that more than 38 million people, representing 59.3% of the United Kingdom population, were living in areas where levels of nitrogen dioxide pollution were above legal limits.
Shadow environment secretary Sue Hayman said: "With almost 40 million people in the United Kingdom living in areas with illegal levels of air pollution, it is simply not acceptable for ministers to hide behind the general election to delay publishing plans to improve air quality".
Despite being ordered to draft a new plan five months ago, the Government left it until last Friday to lodge a request for an extension until June 30 with the High Court.
Furthermore, Sue Hayman, the Labour MP for Workington told Parliament: "Cabinet Office rules are clear that purdah is not an excuse to delay acting on vital public health matters".
She argued that while there are some exceptions to purdah for public health issues "this would generally only apply if there was an unexpected public health emergency".More news: Israel Isolates Hunger Striking Detainees
"We hope that the courts throw out the Government's application and whoever is in power after June 8, puts a stop to all these delaying tactics and gets on with the job in hand, for the benefit of everyone".
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