I assume that the repayment of an increasing national debt depends on an increasing GDP. And increasing GDP, in turn, depends mutatis mutandis on increasing population. So an increase in national debt assumes increasing population and, likewise, a decreasing population would mean both a decrease in GDP per capita and an increase in national debt per capita. Is this, in general, correct?
tl;dr: No, repaying national debt does not assume population increase although depending on the parameters of economy population increase can sometimes help with repaying the debt and also help with reducing the ratio of debt to GDP, but it is neither required nor assumed. Moreover, depending on parameters population growth can even be a hindrance as well.
Full Answer: No the statement in the question is not accurate for several reasons. It is true that GDP depends on population because if every person can produce $\\\$100$ worth of GDP then 10 people will be able to produce $\\\$1000$ of GDP. However, you are incorrect in saying:
decreasing population would mean both a decrease in GDP per capita
because GDP per capita is already calculated as GDP per person. If every person can produce $\\\$100$ then GDP per capita will be $\\\$100$ whether country's population would be ten people or thousands, because GDP per capita is by definition total GDP of a country divided by population.
Furthermore, you seem to be confusing concept of repaying debt with growing out of debt.
From economic perspective what matters the most is the size of debt relative to national income. If a poor person who earns $\\\$200$ a month has debt of $\\\$10000$ that is a problem, but if rich person who earns $\\\$2,000,000$ a month has $\\\$10000$ that is not a problem at all (at least not from economic perspective).
Hence there is a concept of growing out of the debt which says that provided that $GDP$ grows at faster rate than debt the debt to GDP ratio will become smaller and smaller over time. However, this has nothing to do with paying down that debt in principle as the debt is still there and just becomes less economically significant.
From this perspective what matters is what is total GDP and total debt not their per capita counterparts. GDP can grow thanks to population growth but population growth is only one of the factors that can cause GDP to grow. In fact most of GDP growth comes from advancement in technology which makes economies more productive (see Romer's Advanced Macroeconomics). However, at the same time debt can grow with population as well if government borrows to fund policies that depend on size of population (such as healthcare for example) rather ones that have mainly fixed cost such as many public goods like water filtration. Provided that total GDP increases at higher rate as a response to population ($Pop$) growth than total debt $D$ (that is $\partial GDP/ \partial Pop > \partial D /\partial Pop \quad | \partial GDP/ \partial Pop > 0$) it can help to decrease the debt to GDP, but that is not the same as saying it helps to repay debt and even if it helps to reduce debt to GDP ratio it does not mean at all that this ratio cannot be reduced without any population increase. In fact empirically in recent years in developed countries most growth in total GDP comes just from technology/productivity increase as in many developed countries population more or less stagnates but most of them still experience some growth of GDP. Furthermore, note that if $\partial GDP/ \partial Pop > \partial D /\partial Pop \quad | \partial GDP/ \partial Pop > 0$ does not hold population growth can even make the debt to GDP worse.
When we talk about repaying government debt we have to look at government budget constraint. The government budget constrain is given as:
$$G-T=\theta + \beta$$
where $G$ is government spending, $T$ is the net tax revenue after transfers and interest payments, $\theta$ is government financing by high powered money and $\beta$ is government financing by bonds (see for example Blinder & Solow (1973); Christ (1968); Tobin & Buiter (1976).
Government debt is accrued when government issues bonds $\beta>0$ and conversely government debt is repaid when $\beta<0$. Hence in order to see what needs to happen to start repaying the debt we can just solve the budget constraint for $\beta$:
$$G - T- \theta = \beta$$
which tells us that $\beta<0$ when government spending $G$ will be smaller than the amount of taxes $T$ and high powered money $\theta$ government issues (so when $G<T+\theta$). Hence population growth is not necessary for repayment of debt or even assumed. Government will start repaying its debt if its spending is lower than net taxes plus high powered money it issues. Sure if population growth can increase net tax revenue $T$ while not causing government spending $G$ to increase it can help with repaying the debt but it is in no way necessary to assume it will happen for debt to be repaid (and it is also possible that increase in population could lead to more government spending than the increase in tax revenue where population increase would make situation worse).