The SNP leader admitted the word "national" could be "hugely problematic".
6,400 More Train Services To Operate Per Week By 2021
Some 6,400 more train services will be running each week by 2021, according to industry analysis.
The ongoing £50 billion investment in the rail network will result in an 11% rise in the number of weekday services, according to the research.
Operators are already running more than 1,350 more trains each week compared with four years ago, the study found.
The figures were released by the Rail Delivery Group (RDG), representing train companies and Network Rail.
The additional services by 2021 include:
:: An increase in train frequency for London commuters and those on high-speed England to Scotland routes
:: A better timetable for passengers using the Edinburgh to Glasgow and TransPennine routes
:: Further improvements covering Kent, the Midlands, the North West, the West Country and Wales.
Many of the extra services will be operating by 2019.
The ability to run more trains is one of the key benefits of south-east England's Thameslink Programme and Crossrail project.
Punctuality on Britain's rail network is at its lowest point in over a decade.
More than one in 10 (12.3%) trains failed to reach their destinations on time last year, according to the Office of Rail and Road.
This is the worst performance for a 12-month period since the year ending September 2006, when the figure reached 12.5%.
The latest passenger survey by Transport Focus in autumn last year revealed that just 81% are satisfied with the railways, a figure which has not been lower since spring 2007.
RDG chief executive Paul Plummer said: "Rail is an ever more vital public service, enabling jobs, housing and economic growth.
"But there's a capacity crunch affecting the railway, with journeys having doubled in 20 years and the number of trains increasing too.
"That's why we're delivering billions of pounds of improvements and reversing decades of under-investment.
"The £50 billion-plus Railway Upgrade Plan will help ease the congestion on Britain's railway.
"It will break bottlenecks, untangle tracks and harness technology so that more trains can run to more places more often, creating new opportunities and supporting jobs.''
Lianna Etkind of the Campaign for Better Transport welcomed the increase in trains as it would "ease the overcrowding which makes so many commuters' lives a misery''.
But she also called for investment in longer trains and for smaller towns and villages to be better connected with public transport to ensure rail offers a "viable and environmentally responsible alternative to car travel''.
Mick Cash, general secretary of the Rail, Maritime and Transport union, said: "Like most people, we will believe this when we see it. There simply aren't the trains and staff available to make this plan happen.
"Like so much of the spin from our rip-off private train companies, these big promises are doomed to turn to dust.''
Manuel Cortes, general secretary of the Transport Salaried Staffs Association, said: "There is little new in the RDG's announcement of new train services - they are already known to be in the pipeline with services like Crossrail, or the Elizabeth line opening next year.
"While I welcome the RDG's aspiration to bring 6,400 new trains services a week on to our tracks by 2021, I'm weary of their spin.
"I'm sure many passengers, particularly those who commute to work on a daily basis, will be asking themselves why rather than always promising jam tomorrow, they simply just don't get on with running quality train services today.
"Our UK passengers pay the highest fares in Europe for substandard services and I expect they too will respond to this latest 'jam tomorrow' announcement with derision.''
A police watchdog probe was launched after the remains of the 52-year-old were found in a house in Dumfries in February last year.
The accident happened at about 7.50pm on Thursday in Moodiesburn, North Lanarkshire.
More than 70 firefighters were needed to bring the blaze under control at Blochairn Fruit Market in the early hours of Thursday.
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