Watch live: PM to be pressed on prison letters at post-Cabinet press conference

Prime Minister Jacinda Ardern's post-cabinet press conference is likely to be dominated by questions about letters.

Two of the biggest political news stories of the last few days both have written letters at their core.

The first centres around letters sent from accused Christchurch gunman Brenton Tarrant from his prison cell.

Last week, Ardern said the accused should not have been able to express his "hateful views" and said processes needed to be strengthened within prisons to make sure this can never happen again.

Today, Corrections boss Christine Stevenson announced an 0800 number that people can ring if they get a letter from someone in prison they didn't actually know.

Ardern is likely to face questions as to whether this policy goes far enough and if any other measures will be put in place.

The second letter issue is to do with correspondence between Australian talkback radio host Alan Jones and Ardern over comments he made about her last week.

He had said that Australian Prime Minister Scott Morrison should "shove a sock down" Ardern's throat, after she briefly commented on Australia's climate change position.

He has since apologised to Ardern publically but has also sent her a letter.

A spokesperson for Ardern has confirmed Ardern has received the letter but had no further comment to make.

She would not release the letter to The Herald.