Some foreign companies not involved in industries subject to sanctions—especially European consumer-goods firms—have continued operating in Iran despite growing sanctions pressure. Many have been successful.

Paris-listed Groupe Danone S.A. , for example, has a long-standing joint venture that produces Damavand mineral water, Iran’s biggest bottled water brand. Danone increased its stake in that venture to 70% from 40% in 2010. Danone didn’t respond to a request for comment.

Yet even for such companies, sanctions that effectively excised Iran from the global financial system three years ago have caused problems.

The Swiss food and beverage company Nestlé S.A. had to scale back in Iran two years ago when it had trouble moving money out of the country, Iranian traders and a banker told The Wall Street Journal at the time. A Nestlé spokeswoman said the company had around 530 employees in Iran and was there to invest for the long term.

South African mobile phone operator MTN Group took a 49% stake in Irancell in 2005, but weakness in the Iranian rial has hurt its profit, and it has had difficulty repatriating hundreds of millions of dollars of earnings there. MTN Group didn't return a request for comment.

Etihad Airways recently said it would increase the frequency of flights between Abu Dhabi and Tehran from three times a week to daily.

The decision appeared to be an attempt to take advantage of greater Iran-U.S. travel, in anticipation that sanctions would end. Daily flights would give Iranians more direct access to dozens of major U.S. cities, said Kevin Knight, Etihad’s chief strategy and planning officer.

U.S. sanctions are stricter than those imposed by Europe, curtailing almost all dealings with the country. But even some U.S. companies have started to scope it out.

Iranian companies in Dubai have received draft contracts to be official resellers of Hewlett-Packard laptops in Iran, according to Iranian businessmen. And late last year, Dubai-based managers of Hewlett-Packard Development Company L.P. traveled to Tehran to prospect the market and meet Iranian distributors, they said.

HP would be allowed to sell laptops to Iran under a U.S. exemption for consumer electronics decided two years ago, but a thaw between Iran and the West could ease the endeavor. HP declined to comment.

In the event of a final nuclear agreement, lawyers and company executives say the most likely scenario is a gradual but significant inflow of foreign investment. Outsiders not already in Iran will need time to research the market, find local partners and understand the legal environment.

Iran is set up legally for foreign direct investment. Foreigners are allowed to own 100% of their ventures and there are laws to protect them, but the system hasn’t been tested much during the sanctions era.

“There is nothing we can do for the moment and nothing we intend to do before the sanctions are lifted because we don’t want to be in breach of any sanctions,” Albert Momdjian, the founder and chief executive of SOKOTRA Capital Ltd., a Dubai-based private investment firm focused on frontier markets, said Monday. “We’re purely scouting, doing our desktop due diligence in order to better understand and feel the market without investing there yet.”

Mr. Momdjian said the hospitality, tourism, logistics, food and mining sectors in Iran looked particularly attractive.

“Everything needs to be developed,” he said. “The question is to remain focused and have the right local partners.”

—Benoît Faucon contributed reporting from London.