Scandinavian airline SAS said on Sunday that its flight would resume on Tuesday at the earliest and confirmed in a statement on its website on Monday morning that all domestic routes would remain suspended until further notice.
"SAS Scandinavian Airlines would like to inform its customers that all SAS flights are cancelled on April 18 and 19," the company said in a statement.
The exception, it said, were "a few domestic flights in Norway (and) flights from the US departing on April 18 are not cancelled at this time."
SAS flights from New York and Chicago will land in Stockholm on Monday and both are scheduled to depart to the US on time.
"SAS is investigating the possibility to reroute one or more of these flights to Norway," it added.
On Sunday, as the vast cloud of Icelandic volcano ash that has paralysed air travel in Europe shifted, Norway opened a wide stretch of airspace from the central town of Kristiansund up to the northern region of Finnmark.
Sweden also opened a narrow corridor of airspace from Norway to the northern town of Kiruna.