Petry made her surprise announcement after the AfD scored 12.6 percent in Sunday's election, meaning it will be the first far-right party to enter the German parliament in more than half a century.
The far-right has not been represented there since the 1950s - a reflection of Germany's efforts to distance itself from the horrors of the Nazi Holocaust.
Knobloch, President of the Jewish Community of Munich and Upper Bavaria - and former president of the German Jewish Council - said she was deeply concerned about Germany's democracy in light of the exit polls.
Petry pointed to "dissent" within the party, and said there was no point hiding that.
Petry had publically criticized Gauland for saying that the AfD would "go after" the new government and for saying that Germany should be proud of its soldiers in the First and Second World Wars, which she said were not constructive and could push voters away from the party.
But it is hard to know exactly how the party's presence will influence German politics and policy over the next four years.
Knobloch called on the future government and the opposition "to provide non-partisan solutions to the central problems and fears of the people, over terrorism, integration and immigration, internal and external security, poverty, economic stability". Head of the Social Democratic Party Martin Schulz said after the vote that as leader of the party that stood up to Adolf Hitler, he believes that the AfD should be thrown out of parliament.
The AfD - Alternative for Germany - won around 13 per cent of the vote, according to election-night projections.
Seen by many as a fledgling young party from the radical right, the AfD won just 4.7% of the vote in the last federal elections in 2013.
Petry has said the AfD - which other German parties have shunned - should be ready to join coalition governments, while others have said the party should stick to opposition. Exit polls showed that a large part of the AfD's support came from eastern Germany where the economy has lagged behind the rest of the country, while the party's support skewed heavily towards men.
Despite being sister parties, the CDU and CSU have repeatedly clashed in the past two years over Merkel's open-door migration policy.
What does it mean for Germany's political system?
"Today we must be open that there is internal dissent within the AfD", Petry said at the press conference.
Merkel told reporters Monday that the AfD's support in the east was mirrored in some economically depressed areas of the west by voters with similar worries.
Other parties widely condemned the AfD for its rhetoric and radical views during the campaign. The result is a huge victory for the AfD, which was founded in 2013 by anti-eurozone economists but saw a rapid rise in recent years as it embraced an anti-Islam, anti-immigrant platform.
While their nationalist views and harsh line on immigration may echo many of Donald Trump policies, it seems the AfD is not looking to align themselves with the USA president.