Cairn has not included the Arctic territory in a $400m programme of nine oil and gas exploration wells it will drill this year as it ramps up activity around the world.
Last year the Edinburgh-based company said it planned to drill its ninth well off Greenland in 2014.
In yesterday's update Cairn said only that is was maturing plans for the Pitu block, off north-west Greenland, with Norway's Statoil.
A spokesman for the company said Cairn still saw significant potential in Greenland but had been busy finalising planning for the nine wells it would drill in coming months.
Chief executive Simon Thomson said Cairn had the potential to generate more big returns for investors after amassing a portfolio that combines frontier exploration acreage, in places such as Senegal, with lower-risk assets in the North Sea.
The company made its name with a series of bumper finds in India, which funded payouts to investors worth around £2.2bn in 2011.
It launched a $300m share buy back programme in October.
"Over the past 12 months, Cairn has built a long-term sustainable business," said Mr Thomson. "The exploration programme will provide investors with exposure to material growth potential alongside mature basin development and pre-development assets, all against a backdrop of continued balance sheet strength."
This year's drilling programme includes three exploration wells in the UK North Sea and one in Norwegian waters.
Cairn acquired extensive acreage in the North Sea through the takeover of Agora Oil & Gas and Nautical Petroleum in 2012, for around £700m in total. The company has been pleased with the progress it has made in the area and hopes to develop a series of fields that could be used to generate cash to fund exploration work around the world.
Cairn Energy and Enquest have won UK Government approval to develop the £4bn Kraken heavy oil field east of Shetland. First oil is expected by summer 2017, with Cairn's share forecast to be 12,500 barrel oil per day.
It expects a development plan for the Catcher field, east of Aberdeen, to be submitted to the Government in the first quarter.
The results of recent appraisal drilling on the Skarfjell find made off Norway following the acquisition of Agora were encouraging.
Cairn was so impressed it has agreed to acquire a 20% interest in the nearby Atlas prospect, for an undisclosed sum.
It was awarded three more Norwegian licences yesterday.
The company has planned an active drilling programme on the licences it has acquired in relatively under-explored areas of the Atlantic Margin, where Cairn's geologists believe there is potential to make big finds.
It will drill two wells each off Morocco and Senegal this year, and one west of Ireland.
While Cairn has made hefty investments in recent years it remains in a strong financial position.
The company sold a controlling stake in its former Indian subsidiary to Vedanta Resources for $5.4bn (£3.3bn) in 2011.
It had net cash of $1.25bn at 31 December.
The company's remaining 10% holding in Cairn India Limited was valued at around $1.0bn at 31 December.
Cairn drilled eight wells off Greenland in 2010 and 2011.It plugged and abandoned the last two in November 2011.
However Mr Thomson noted then that Cairn had found traces of hydrocarbons in several places.
In January last year Cairn said: "Both Cairn and partners Statoil and Nunaoil continue to be encouraged by the opportunity in Pitu and are targeting exploration drilling in 2014, subject to Government approval."
In August the company said it would make a decision with Statoil in the second half of 2013 about drilling a well off Greenland this year.
The company's campaign off Greenland has been criticised by Greenpeace, which claims drilling in the area entails big risks for the environment. Cairn Energy has said it is operating under some of the most stringent standards worldwide.
Analysts at joint house broker Morgan Stanley described Cairn's exploration programme as "potentially transformational".
Shares in Cairn Energy closed down 3.2p at 263.5p.